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Тр. МИАН, 2001, том 234, страницы 3–383
(Mi tm230)
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Эта публикация цитируется в 466 научных статьях (всего в 467 статьях)
Априорные оценки и отсутствие решений нелинейных уравнений и неравенств в частных производных
Э. Митидиериa, С. И. Похожаевb a University of Trieste
b Математический институт им. В. А. Стеклова РАН
Аннотация:
Предлагается общий подход к априорным оценкам решений нелинейных уравнений и неравенств в частных производных. Рассматриваются их приложения к проблеме отсутствия решений. Метод основан на концепции нелинейной емкости, порождаемой нелинейным дифференциальным оператором. Содержание тома разбито на три части, посвященные эллиптическим, параболическим и гиперболическим нелинейным проблемам.
Для специалистов по нелинейным уравнениям с частными производными, математической физике и прикладной математике, а также аспирантов и студентов старших курсов соответствующих специальностей.
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Англоязычная версия:
Proceedings of the Steklov Institute of Mathematics, 2001, 234, 1–362
Реферативные базы данных:
Тип публикации:
Книга
УДК:
517
Образец цитирования:
Э. Митидиери, С. И. Похожаев, “Априорные оценки и отсутствие решений нелинейных уравнений и неравенств в частных производных”, Тр. МИАН, 234, Наука, МАИК «Наука/Интерпериодика», М., 2001, 3–383; Proc. Steklov Inst. Math., 234 (2001), 1–362
Цитирование в формате AMSBIB
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\paper Априорные оценки и отсутствие решений нелинейных уравнений и неравенств в~частных производных
\serial Тр. МИАН
\yr 2001
\vol 234
\pages 3--383
\publ Наука, МАИК «Наука/Интерпериодика»
\publaddr М.
\mathnet{http://mi.mathnet.ru/tm230}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1879326}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2001
\vol 234
\pages 1--362
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Galaktionov V.A., Pohozaev S.I., “Blow–up and critical exponents for parabolic equations with non–divergent operators: dual porous medium and thin film operators”, Journal of Evolution Equations, 6:1 (2006), 45–69
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Lupo D., Payne K.R., Popivanov N.I., “Nonexistence of nontrivial solutions for supercritical equations of mixed elliptic-hyperbolic type”, Contributions to Nonlinear Analysis - A TRIBUTE TO D. G. DE FIGUEIREDO ON THE OCCASION OF HIS 70TH BIRTHDAY, Progress in Nonlinear Differential Equations and their Applications, 66, 2006, 371–390
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Caristi G., Mitidieri E., “Harnack inequality and applications to solutions of biharmonic equations”, Partial Differential Equations and Functional Analysis: The Philippe Clement Festschrift, Operator Theory : Advances and Applications, 168, 2006, 1–26
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Liskevich V., Lyakhova S., Moroz V., “Positive Solutions to Singular Semilinear Elliptic Equations with Critical Potential on Cone-Like Domains”, Adv. Differ. Equat., 11:4 (2006), 361–398
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А. А. Коньков, “Поведение решений эллиптических неравенств, нелинейных
относительно старших производных”, Изв. РАН. Сер. матем., 71:1 (2007), 17–54
; A. A. Kon'kov, “The behaviour of solutions of elliptic inequalities that are non-linear with respect to the highest derivatives”, Izv. Math., 71:1 (2007), 15–51 -
Bogveradze G., Kharibegashvili S., “On the global and local solution of the multidimensional Darboux problem for some nonlinear wave equations”, Georgian Mathematical Journal, 14:1 (2007), 65–80
-
Polacik P., Quittner P., Souplet Ph., “Singularity and decay estimates in superlinear problems via Liouville–type theorems, I: Elliptic equations and systems”, Duke Mathematical Journal, 139:3 (2007), 555–579
-
Galaktionov V.A., Pohozaev S.I., “Blowup for nonlinear initial–boundary value problems”, Doklady Mathematics, 75:1 (2007), 76–79
-
Kharibegashvili S.S., “On the existence or absence of global solutions for the multidimensional version of the second Darboux problem for some nonlinear hyperbolic equations”, Differential Equations, 43:3 (2007), 402–416
-
Ferrero A., Grunau H.-Ch., “The Dirichlet problem for supercritical biharmonic equations with power–type nonlinearity”, Journal of Differential Equations, 234:2 (2007), 582–606
-
Surnachev M.D., Filimonova I.V., “Existence of positive solutions of a semilinear nondivergence form elliptic equation in a conical domain”, Differential Equations, 43:1 (2007), 147–150
-
Liskevich V., Lyakhova S., Moroz V., “Positive solutions to nonlinear p–Laplace equations with Hardy potential in exterior domains”, Journal of Differential Equations, 232:1 (2007), 212–252
-
Gazzola F., Grunau H.-Ch., “Global solutions for superlinear parabolic equations involving the biharmonic operator for initial data with optimal slow decay”, Calculus of Variations and Partial Differential Equations, 30:3 (2007), 389–415
-
Xiang Zh., Mu Ch., Du L., “A Liouville–type theorem for a system of parabolic inequalities and its applications”, Applied Mathematics Letters, 20:9 (2007), 976–981
-
Bagyrov Sh.G., “On the existence of a positive solution of a nonlinear second–order parabolic equation with time–periodic coefficients”, Differential Equations, 43:4 (2007), 581–585
-
Galakhov E., “Some nonexistence results for quasilinear PDE's”, Communications on Pure and Applied Analysis, 6:1 (2007), 141–161
-
Kon'kov A.A., “Comparison theorems for elliptic inequalities with a non–linearity in the principal part”, Journal of Mathematical Analysis and Applications, 325:2 (2007), 1013–1041
-
Kaikina E.I., “Nonlinear pseudoparabolic type equations on a half-line with large initial data”, Nonlinear Analysis-Theory Methods & Applications, 67:10 (2007), 2839–2858
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Yuri Bozhkov, Enzo Mitidieri, “Lie Symmetries and Criticality of Semilinear Differential Systems”, SIGMA, 3 (2007), 053, 17 pp.
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И. В. Асташова, “Равномерные оценки решений квазилинейных дифференциальных неравенств”, Тр. сем. им. И. Г. Петровского, 26, Изд-во Моск. ун-та, М., 2007, 29–38
; I. V. Astashova, “Uniform estimates of positive solutions to quasi-linear differential equations”, J. Math. Sci. (N. Y.), 143:4 (2007), 3198–3204 -
В. А. Галактионов, С. И. Похожаев, “Об отсутствии глобальных решений нелинейных смешанных задач”, Тр. сем. им. И. Г. Петровского, 26, Изд-во Моск. ун-та, М., 2007, 73–91
; V. A. Galaktionov, S. I. Pokhozhaev, “On the absence of global solutions of nonlinear mixed problems”, J. Math. Sci. (N. Y.), 143:4 (2007), 3226–3238 -
G. Caristi, L. D'Ambrosio, E. Mitidieri, “Liouville Theorems for Some Nonlinear Inequalities”, Теория функций и нелинейные уравнения в частных производных, Сборник статей. К 70-летию со дня рождения члена-корреспондента РАН Станислава Ивановича Похожаева, Тр. МИАН, 260, МАИК «Наука/Интерпериодика», М., 2008, 97–118
; Proc. Steklov Inst. Math., 260 (2008), 90–111 -
Е. И. Галахов, “О дифференциальных неравенствах с точечными особенностями на границе”, Теория функций и нелинейные уравнения в частных производных, Сборник статей. К 70-летию со дня рождения члена-корреспондента РАН Станислава Ивановича Похожаева, Тр. МИАН, 260, МАИК «Наука/Интерпериодика», М., 2008, 119–129
; E. I. Galakhov, “On Differential Inequalities with Point Singularities on the Boundary”, Proc. Steklov Inst. Math., 260 (2008), 112–122 -
V. A. Galaktionov, “On Nonexistence of Baras–Goldstein Type without Positivity Assumptions for Singular Linear and Nonlinear Parabolic Equations”, Теория функций и нелинейные уравнения в частных производных, Сборник статей. К 70-летию со дня рождения члена-корреспондента РАН Станислава Ивановича Похожаева, Тр. МИАН, 260, МАИК «Наука/Интерпериодика», М., 2008, 130–150
; Proc. Steklov Inst. Math., 260 (2008), 123–143 -
С. И. Похожаев, “О разрушении решений нелинейных смешанных задач”, Теория функций и нелинейные уравнения в частных производных, Сборник статей. К 70-летию со дня рождения члена-корреспондента РАН Станислава Ивановича Похожаева, Тр. МИАН, 260, МАИК «Наука/Интерпериодика», М., 2008, 213–226
; S. I. Pokhozhaev, “On the Blow-up of Solutions to Nonlinear Initial–Boundary Value Problems”, Proc. Steklov Inst. Math., 260 (2008), 204–217 -
И. В. Асташова, “Равномерные оценки положительных решений квазилинейных дифференциальных уравнений высокого порядка”, Дифференциальные уравнения и динамические системы, Сборник статей, Тр. МИАН, 261, МАИК «Наука/Интерпериодика», М., 2008, 26–36
; I. V. Astashova, “Uniform Estimates for Positive Solutions of Higher Order Quasilinear Differential Equations”, Proc. Steklov Inst. Math., 261 (2008), 22–33 -
А. А. Коньков, “Об отсутствии глобальных решений у радиального уравнения $p$-Лапласа”, УМН, 63:1(379) (2008), 161–162
; A. A. Kon'kov, “On the absence of global solutions of the radial $p$-Laplace equation”, Russian Math. Surveys, 63:1 (2008), 161–162 -
С. И. Похожаев, “О разрушении решений уравнения Курамото–Сивашинского”, Матем. сб., 199:9 (2008), 97–106
; S. I. Pokhozhaev, “On blow-up of solutions of the Kuramoto-Sivashinsky equation”, Sb. Math., 199:9 (2008), 1355–1365 -
О. М. Джохадзе, С. С. Харибегашвили, “О первой задаче Дарбу для нелинейных гиперболических уравнений второго порядка”, Матем. заметки, 84:5 (2008), 693–712
; O. M. Dzhokhadze, S. S. Kharibegashvili, “First Darboux Problem for Nonlinear Hyperbolic Equations of Second Order”, Math. Notes, 84:5 (2008), 646–663 -
И. В. Асташова, “Равномерные оценки положительных решений квазилинейных обыкновенных дифференциальных уравнений”, Изв. РАН. Сер. матем., 72:6 (2008), 85–104
; I. V. Astashova, “Uniform estimates for positive solutions of quasi-linear ordinary differential equations”, Izv. Math., 72:6 (2008), 1141–1160 -
Galaktionov, VA, “CAPACITY INDUCED BY A NONLINEAR OPERATOR AND APPLICATIONS”, Georgian Mathematical Journal, 15:3 (2008), 501
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Caristi, G, “Representation Formulae for Solutions to Some Classes of Higher Order Systems and Related Liouville Theorems”, Milan Journal of Mathematics, 76:1 (2008), 27
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Dechevski L., Popivanov N., “Morawetz–Protter 3D Problem for Quasilinear Equations of Elliptic–Hyperbolic Type. Critical and Supercritical Cases”, Comptes Rendus de l Academie Bulgare Des Sciences, 61:12 (2008), 1501–1508
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Dechevsky L.T., Popivanov N., “Quasilinear Equations of Elliptic–Hyperbolic Type. Critical 2D Case for Nontrivial Solutions”, Comptes Rendus de l Academie Bulgare Des Sciences, 61:11 (2008), 1385–1392
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Pohozaev S.I., “On the nonexistence of global solutions of the Hamilton–Jacobi equation”, Differential Equations, 44:10 (2008), 1467–1477
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Kharibegashvili S., Midodashvili B., “On One Boundary Value Problem for a Nonlinear Equation with the Iterated Wave Operator in the Principal Part”, Georgian Mathematical Journal, 15:3 (2008), 541–554
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Avila A.I., Brock F., “Asymptotics at infinity of solutions for p–Laplace equations in exterior domains”, Nonlinear Analysis–Theory Methods & Applications, 69:5–6 (2008), 1615–1628
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Berikelashvili G.K., Dzhokhadze O.M., Midodashvili B.G., Kharibegashvili S.S., “On the existence and absence of global solutions of the first Darboux problem for nonlinear wave equations”, Differential Equations, 44:3 (2008), 374–389
-
Tatar N.-e., “Nonexistence results for a fractional problem arising in thermal diffusion in fractal media”, Chaos Solitons & Fractals, 36:5 (2008), 1205–1214
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Kharibegashvili S.S., “On the solvability of the characteristic cauchy problem for some nonlinear wave equations in the future light cone”, Differential Equations, 44:1 (2008), 135–146
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Sirakov B., “Existence results and a priori bounds for higher order elliptic equations and systems”, Journal de Mathematiques Pures et Appliquees, 89:2 (2008), 114–133
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Kharibegashvili S., “On the solvability of one multidimensional version of the first Darboux problem for some nonlinear wave equations”, Nonlinear Analysis–Theory Methods & Applications, 68:4 (2008), 912–924
-
Kharibegashvili S., “On the solvability of the Cauchy characteristic problem for a nonlinear equation with iterated wave operator in the principal part”, Journal of Mathematical Analysis and Applications, 338:1 (2008), 71–81
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Galaktionov V.A., “Hermitian Spectral Theory and Blow–Up Patterns for a Fourth–Order Semilinear Boussinesq Equation”, Studies in Applied Mathematics, 121:4 (2008), 395–431
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Jokhadze O., Midodashvili B., “The first Darboux problem for wave equations with a nonlinear positive source term”, Nonlinear Analysis–Theory Methods & Applications, 69:9 (2008), 3005–3015
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Toscano L., “Absence of Global Solutions to Systems of Perturbed Parabolic Inequalities with Chipot–Weissler Nonlinearity in the Gradient Term”, Advanced Nonlinear Studies, 8:4 (2008), 679–718
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Musina R., “Ground state solutions of a critical problem involving cylindrical weights”, Nonlinear Analysis–Theory Methods & Applications, 68:12 (2008), 3972–3986
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Galaktionov V.A., Mitidieri E., Pohozaev S.I., “Existence and nonexistence of a global solution to the Kuramoto–Sivashinsky equation”, Doklady Mathematics, 77:2 (2008), 238–242
-
Caristi G., Mitidieri E., Pohozaev S.I., “Local estimates and Liouville theorems for a class of quasilinear inequalities”, Doklady Mathematics, 77:1 (2008), 85–89
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Jokhadze O., “On existence and nonexistence of global solutions of Cauchy–Goursat problem for nonlinear wave equations”, Journal of Mathematical Analysis and Applications, 340:2 (2008), 1033–1045
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С. И. Похожаев, “Об отсутствии положительных решений эллиптических уравнений в плоских неограниченных областях”, Матем. заметки, 85:2 (2009), 261–272
; S. I. Pokhozhaev, “On the Absence of Positive Solutions of Elliptic Equations in Plane Unbounded Domains”, Math. Notes, 85:2 (2009), 240–250 -
М. О. Корпусов, А. Г. Свешников, “О разрушении решения системы уравнений Осколкова”, Матем. сб., 200:4 (2009), 83–108
; M. O. Korpusov, A. G. Sveshnikov, “Blow-up of Oskolkov's system of equations”, Sb. Math., 200:4 (2009), 549–572 -
Caristi, G, “Some Liouville theorems for quasilinear elliptic inequalities”, Doklady Mathematics, 79:1 (2009), 118
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Е. И. Галахов, “Об отсутствии локальных решений некоторых эволюционных задач”, Матем. заметки, 86:3 (2009), 337–349
; E. I. Galakhov, “On the Absence of Local Solutions of Several Evolutionary Problems”, Math. Notes, 86:3 (2009), 314–324 -
Е. И. Кайкина, П. И. Наумкин, И. А. Шишмарев, “Асимптотика решений при больших временах для нелинейных уравнений типа Соболева”, УМН, 64:3(387) (2009), 3–72
; E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev, “Large-time asymptotic behaviour of solutions of non-linear Sobolev-type equations”, Russian Math. Surveys, 64:3 (2009), 399–468 -
Е. И. Галахов, “Об эллиптических и параболических неравенствах с точечными особенностями на границе”, Матем. сб., 200:10 (2009), 3–24
; E. I. Galakhov, “Elliptic and parabolic inequalities with point singularities on the boundary”, Sb. Math., 200:10 (2009), 1417–1437 -
Mitidieri E., Pokhozhaev S.I., “Lifespan estimates for solutions of some evolution inequalities”, Differential Equations, 45:10 (2009), 1473–1484
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Lyberopoulos A.N., “Existence and Liouville–type theorems for some indefinite quasilinear elliptic problems with potentials vanishing at infinity”, Journal of Functional Analysis, 257:11 (2009), 3593–3616
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Davila J., Flores I., Guerra I., “Multiplicity of solutions for a fourth order problem with exponential nonlinearity”, Journal of Differential Equations, 247:11 (2009), 3136–3162
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Korpusov M.O., Sveshnikov A.G., “Application of the Nonlinear Capacity Method to Differential Inequalities of Sobolev Type”, Differential Equations, 45:7 (2009), 951–959
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Filippucci R., Pucci P., Rigoli M., “On entire solutions of degenerate elliptic differential inequalities with nonlinear gradient terms”, Journal of Mathematical Analysis and Applications, 356:2 (2009), 689–697
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Chen W., Li C., “An Integral System and the Lane–Emden Conjecture”, Discrete and Continuous Dynamical Systems, 24:4 (2009), 1167–1184
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Quaas A., Sirakov B., “Existence and Non–existence Results for Fully Nonlinear Elliptic Systems”, Indiana University Mathematics Journal, 58:2 (2009), 751–788
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D'Ambrosio L., “Liouville theorems for anisotropic quasilinear inequalities”, Nonlinear Analysis–Theory Methods & Applications, 70:8 (2009), 2855–2869
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Filippucci R., “Nonexistence of positive weak solutions of elliptic inequalities”, Nonlinear Analysis–Theory Methods & Applications, 70:8 (2009), 2903–2916
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Filippucci R., Pucci P., Rigoli M., “On weak solutions of nonlinear weighted p–Laplacian elliptic inequalities”, Nonlinear Analysis–Theory Methods & Applications, 70:8 (2009), 3008–3019
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Kon'kov A.A., “On global solutions of the radial p–Laplace equation”, Nonlinear Analysis–Theory Methods & Applications, 70:10 (2009), 3437–3451
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Aliev A.B., Kazymov A.A., “Global Weak Solutions of the Cauchy Problem for Semilinear Pseudo–Hyperbolic Equations”, Differential Equations, 45:2 (2009), 175–185
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Serrin J., “Entire solutions of quasilinear elliptic equations”, Journal of Mathematical Analysis and Applications, 352:1 (2009), 3–14
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Cassani D., do O J.M., Ghoussoub N., “On a Fourth Order Elliptic Problem with a Singular Nonlinearity”, Advanced Nonlinear Studies, 9:1 (2009), 177–197
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Li Yuxiang, “Optimal conditions for L–infinity–regularity and a priori estimates for semilinear elliptic systems”, Journal of Mathematical Analysis and Applications, 351:1 (2009), 257–276
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Kondratiev V., Liskevich V., Sobol Z., “Positive Super–Solutions to Semi–Linear Second–Order Non–Divergence Type Elliptic Equations in Exterior Domains”, Transactions of the American Mathematical Society, 361:2 (2009), 697–713
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Ferrero A., Grunau H.-Ch., Karageorgis P., “Supercritical biharmonic equations with power–type nonlinearity”, Annali Di Matematica Pura Ed Applicata, 188:1 (2009), 171–185
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Vetois J., “A priori estimates for solutions of anisotropic elliptic equations”, Nonlinear Analysis–Theory Methods & Applications, 71:9 (2009), 3881–3905
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Pohozaev S.I., “Critical Nonlinearities in Partial Differential Equations”, Milan Journal of Mathematics, 77:1 (2009), 127–150
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Yakubov A.Ya., “On nonlinear Volterra equations of convolution type”, Differential Equations, 45:9 (2009), 1326–1336
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Galaktionov V.A., “Five types of blow–up in a semilinear fourth–order reaction–diffusion equation: an analytic–numerical approach”, Nonlinearity, 22:7 (2009), 1695–1741
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Galakhov E., “A comparison principle for quasilinear operators in unbounded domains”, Nonlinear Analysis–Theory Methods & Applications, 70:12 (2009), 4190–4194
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Galaktionov V.A., Mitidieri E., Pohozaev S.I., “On global solutions and blow–up for Kuramoto–Sivashinsky–type models, and well–posed Burnett equations”, Nonlinear Analysis–Theory Methods & Applications, 70:8 (2009), 2930–2952
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Galaktionov V.A., “Three types of self–similar blow–up for the fourth–order p–Laplacian equation with source”, Journal of Computational and Applied Mathematics, 223:1 (2009), 326–355
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Jokhadze O., “Cauchy-Goursat Problem for One-Dimensional Semilinear Wave Equations”, Communications in Partial Differential Equations, 34:4 (2009), 367–382
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Galakhov E.I., “Blow-up of solutions of some nonlinear wave equations”, Differential Equations, 45:1 (2009), 59–67
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А. А. Коньков, “Теоремы сравнения для квазилинейных эллиптических неравенств”, Матем. заметки, 87:4 (2010), 630–631
; A. A. Kon'kov, “Comparison Theorems for Quasilinear Elliptic Inequalities”, Math. Notes, 87:4 (2010), 588–589 -
Pohozaev S.I., “On the blow–up of sign–changing solutions to semilinear parabolic equations”, Doklady Mathematics, 81:2 (2010), 185–187
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Garcia-Melian J., Quiros F., “Fujita exponents for evolution problems with nonlocal diffusion”, Journal of Evolution Equations, 10:1 (2010), 147–161
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Aliev A.B., Lichaei B.H., “Existence and non–existence of global solutions of the Cauchy problem for higher order semilinear pseudo–hyperbolic equations”, Nonlinear Analysis–Theory Methods & Applications, 72:7–8 (2010), 3275–3288
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Laskri Ya., Tatar N.-e., “The critical exponent for an ordinary fractional differential problem”, Computers & Mathematics With Applications, 59:3 (2010), 1266–1270
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Kon'kov A.A., “On global solutions of the radial p–Laplace equation. The case of large p”, Nonlinear Analysis–Theory Methods & Applications, 72:3–4 (2010), 2047–2062
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Mari L., Rigoli M., Setti A.G., “Keller–Osserman conditions for diffusion–type operators on Riemannian manifolds”, Journal of Functional Analysis, 258:2 (2010), 665–712
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Berchio E., Cassani D., Gazzola F., “Hardy–Rellich inequalities with boundary remainder terms and applications”, Manuscripta Mathematica, 131:3–4 (2010), 427–458
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С. И. Похожаев, “Об одном уравнении теории горения”, Матем. заметки, 88:1 (2010), 53–62
; S. I. Pokhozhaev, “Concerning an Equation in the Theory of Combustion”, Math. Notes, 88:1 (2010), 48–56 -
Е. И. Галахов, “Об эллиптических и параболических неравенствах высокого порядка с сингулярностями на границе”, Теория функций и дифференциальные уравнения, Сборник статей. К 105-летию со дня рождения академика Сергея Михайловича Никольского, Тр. МИАН, 269, МАИК «Наука/Интерпериодика», М., 2010, 82–90
; E. I. Galakhov, “On higher order elliptic and parabolic inequalities with singularities on the boundary”, Proc. Steklov Inst. Math., 269 (2010), 76–84 -
С. И. Похожаев, “Разрушение знакопеременных решений квазилинейных параболических уравнений”, Теория функций и дифференциальные уравнения, Сборник статей. К 105-летию со дня рождения академика Сергея Михайловича Никольского, Тр. МИАН, 269, МАИК «Наука/Интерпериодика», М., 2010, 215–224
; S. I. Pohozaev, “Blow-up of sign-changing solutions to quasilinear parabolic equations”, Proc. Steklov Inst. Math., 269 (2010), 208–217 -
С. И. Похожаев, “О сингулярных решениях уравнения Кортевега–де Фриза”, Матем. заметки, 88:5 (2010), 770–777
; S. I. Pokhozhaev, “On the Singular Solutions of the Korteweg–de Vries Equation”, Math. Notes, 88:5 (2010), 741–747 -
П. П. Матус, “О корректности разностных схем для полулинейного параболического уравнения с обобщенными решениями”, Ж. вычисл. матем. и матем. физ., 50:12 (2010), 2155–2175
; P. P. Matus, “Well-posedness of difference schemes for semilinear parabolic equations with weak solutions”, Comput. Math. Math. Phys., 50:12 (2010), 2044–2063 -
Chen C., Wang Zh., Wang F., “Existence and Nonexistence of Positive Solutions for Singular p-Laplacian Equation in R-N”, Bound Value Probl, 2010, 607453
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Galaktionov V.A., Kamotski I.V., “On Nonexistence of Baras-Goldstein Type for Higher-Order Parabolic Equations with Singular Potentials”, Trans Amer Math Soc, 362:8 (2010), 4117–4136
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Gazzola F., Grunau H.-Ch., Sweers G., “Models of Higher Order”, Polyharmonic Boundary Value Problems, Lecture Notes in Mathematics, 1991, 2010, 1
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Fino A., Karch G., “Decay of mass for nonlinear equation with fractional Laplacian”, Monatsh Math, 160:4 (2010), 375–384
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Davila J., Flores I., Guerra I., “Multiplicity of solutions for a fourth order equation with power-type nonlinearity”, Math Ann, 348:1 (2010), 143–193
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Antontsev S., Shmarev S., “Blow-up of solutions to parabolic equations with nonstandard growth conditions”, J Comput Appl Math, 234:9 (2010), 2633–2645
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Filippucci R., Pucci P., Rigoli M., “Nonlinear Weighted P-Laplacian Elliptic Inequalities with Gradient Terms”, Commun Contemp Math, 12:3 (2010), 501–535
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Pokhozhaev S.I., “On stationary solutions of the Vlasov–Poisson equations”, Differ Equ, 46:4 (2010), 530–537
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Dancer E.N., Wei J., Weth T., “A priori bounds versus multiple existence of positive solutions for a nonlinear Schrodinger system”, Ann Inst H Poincaré Anal Non Linéaire, 27:3 (2010), 953–969
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Galaktionov V.A., “Incomplete Self-Similar Blow-Up in a Semilinear Fourth-Order Reaction-Diffusion Equation”, Stud Appl Math, 124:4 (2010), 347–381
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Aliev A.B., Mamedov F.V., “Existence and nonexistence of global solutions of the cauchy problem for semilinear hyperbolic equations with dissipation and with anisotropic elliptic part”, Differ Equ, 46:3 (2010), 309–320
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Ambrosio Lorenzo D', Mitidieri E., “A priori estimates, positivity results, and nonexistence theorems for quasilinear degenerate elliptic inequalities”, Adv Math, 224:3 (2010), 967–1020
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Г. А. Рудых, “Анализ стационарных решений начально-краевой задачи для нелокального параболического уравнения физики плазмы”, Известия Иркутского государственного университета. Серия Математика, 3:2 (2010), 61–87
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М. О. Корпусов, “О разрушении ионно-звуковых волн в плазме”, Матем. сб., 202:1 (2011), 37–64
; M. O. Korpusov, “Blow-up of ion acoustic waves in a plasma”, Sb. Math., 202:1 (2011), 35–60 -
С. И. Похожаев, “О некоторых весовых тождествах для решений обобщенных уравнений Кортевега–де Фриза”, Матем. заметки, 89:3 (2011), 393–409
; S. I. Pokhozhaev, “Weighted Identities for the Solutions of Generalized Korteweg–de Vries Equations”, Math. Notes, 89:3 (2011), 382–396 -
М. О. Корпусов, А. Г. Свешников, “Об эффекте релаксации за конечное время решения нелинейного псевдопараболического уравнения”, Ж. вычисл. матем. и матем. физ., 51:3 (2011), 407–435
; M. O. Korpusov, A. G. Sveshnikov, “Finite-time relaxation of the solution of a nonlinear pseudoparabolic equation”, Comput. Math. Math. Phys., 51:3 (2011), 377–403 -
М. О. Корпусов, “О разрушении решений волновых уравнений в системах с распределенными параметрами”, ТМФ, 167:2 (2011), 206–213
; M. O. Korpusov, “Destruction of solutions of wave equations in systems with distributed parameters”, Theoret. and Math. Phys., 167:2 (2011), 577–583 -
С. И. Похожаев, “Об отсутствии глобальных решений уравнения Кортевега–де Фриза”, Уравнения в частных производных, СМФН, 39, РУДН, М., 2011, 141–150
; S. I. Pohozaev, “On the absence of global solutions of the Korteweg–de Vries equation”, Journal of Mathematical Sciences, 190:1 (2013), 147–156 -
Farina A., Serrin J., “Entire solutions of completely coercive quasilinear elliptic equations”, J Differential Equations, 250:12 (2011), 4367–4408
-
Jeanjean L., Squassina M., “An approach to minimization under a constraint: the added mass technique”, Calc Var Partial Differential Equations, 41:3–4 (2011), 511–534
-
Lan K.Q., “Positive weak solutions of semilinear second order elliptic inequalities via variational inequalities”, J Math Anal Appl, 380:2 (2011), 520–530
-
Kharibegashvili S., Midodashvili B., “On the solvability of one boundary value problem for some semilinear wave equations with source terms”, NoDEA Nonlinear Differential Equations Appl, 18:2 (2011), 117–138
-
Surnachev M., “Asymptotic behaviour of solutions of nondivergence type semilinear elliptic equations in conical domains I”, Asymptot Anal, 71:4 (2011), 227–243
-
Chen C., Shi L., Zhu Sh., “Nonexistence of positive entire solutions for a class of (p, q)-Laplacian elliptic systems”, Appl Math Lett, 24:6 (2011), 831–837
-
Li X., Li F., “A priori estimates for nonlinear differential inequalities and applications”, J Math Anal Appl, 378:2 (2011), 723–733
-
Chen C., Zhu Sh., Shi L., “Remarks on nonexistence of solutions of mixed sublinear and superlinear elliptic equation in R-N”, J Math Anal Appl, 379:1 (2011), 8–14
-
Lazzo M., Schmidt P.G., “Periodic Solutions and Invariant Manifolds for an Even-Order Differential Equation with Power Nonlinearity”, J Dynam Differential Equations, 23:1 (2011), 141–166
-
Kharibegashvili S., Midodashvili B., “Global solvability of the Cauchy characteristic problem for one class of nonlinear second order hyperbolic systems”, J Math Anal Appl, 376:2 (2011), 750–759
-
Magliaro M., Mari L., Mastrolia P., Rigoli M., “Keller-Osserman type conditions for differential inequalities with gradient terms on the Heisenberg group”, J Differential Equations, 250:6 (2011), 2643–2670
-
Filippucci R., “Nonexistence of nonnegative solutions of elliptic systems of divergence type”, J Differential Equations, 250:1 (2011), 572–595
-
М. О. Корпусов, “О разрушении решения одной системы уравнений ионно-звуковых волн в плазме”, Сиб. матем. журн., 52:3 (2011), 600–614
; M. O. Korpusov, “On blowup of solutions to a system of equations of ion sound waves in plasma”, Siberian Math. J., 52:3 (2011), 471–483 -
М. О. Корпусов, “О разрушении внутренних гравитационных волн с нелинейными источниками”, Изв. РАН. Сер. матем., 75:4 (2011), 29–48
; M. O. Korpusov, “On the blow-up of internal gravitational waves with non-linear sources”, Izv. Math., 75:4 (2011), 691–710 -
М. О. Корпусов, “О разрушении гравитационно-гироскопических волн с нелинейными источниками и стоками на границе”, Матем. тр., 14:2 (2011), 83–126
; M. O. Korpusov, “On blowup of gravity-gyroscopic waves with nonlinear sources and sinks on the boundary”, Siberian Adv. Math., 22:3 (2012), 161–191 -
И. Г. Царьков, “Устойчивость однозначной разрешимости квазилинейных уравнений по дополнительной информации”, Матем. заметки, 90:6 (2011), 918–946
; I. G. Tsar'kov, “Stability of Unique Solvability of Quasilinear Equations Given Additional Data”, Math. Notes, 90:6 (2011), 894–919 -
М. О. Корпусов, “О разрушении ионно-звуковых волн в плазме с сильной пространственно-временной дисперсией”, Алгебра и анализ, 23:6 (2011), 96–130
; M. O. Korpusov, “Blow up of ion-acoustic waves in plasma with strong time-spatial dispertion”, St. Petersburg Math. J., 23:6 (2012), 989–1011 -
Харибегашвили С.С., Джохадзе О.М., “Задача Коши для лобобщенного нелинейного уравнения Лиувилля”, Дифференциальные уравнения, 47:12 (2011), 1741
; Kharibegashvili S.S., Dzhokhadze O.M., “Cauchy Problem for a Generalized Nonlinear Liouville Equation”, Differ Equ, 47:12 (2011), 1763–1775 -
Armstrong S.N., Sirakov B., “Nonexistence of Positive Supersolutions of Elliptic Equations via the Maximum Principle”, Comm Partial Differential Equations, 36:11 (2011), 2011–2047
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Похожаев С.И., “О зависимости критического показателя нелинейного уравнения теплопроводности от начальной функции”, Дифференциальные уравнения, 47:7 (2011), 946–953
; Pokhozhaev S.I., “On the Dependence of the Critical Exponent of the Nonlinear Heat Equation on the Initial Function”, Differ Equ, 47:7 (2011), 955–962 -
Antontsev S., “Wave equation with p(x, t)-Laplacian and damping term: Blow-up of solutions”, Comptes Rendus Mecanique, 339:12 (2011), 751–755
-
Armstrong S.N., Sirakov B., “Sharp Liouville results for fully nonlinear equations with power-growth nonlinearities”, Ann Sc Norm Super Pisa Cl Sci, 10:3 (2011), 711–728
-
Li J., Yin J., Jin Ch., “Blow-up and global existence profile of a class of fully nonlinear degenerate parabolic equations”, Cent Eur J Math, 9:6 (2011), 1435–1447
-
Kerbal S., Kirane M., “Nonexistence Results for the Cauchy Problem for Nonlinear Ultraparabolic Equations”, Abstr Appl Anal, 2011, 149091
-
Berbiche M., “Nonexistence of Solutions Results for Certain Fractional Differential Equations”, Math Model Anal, 16:3 (2011), 488–497
-
Ghoul T.-e., “An extension of Dickstein's “small lambda” theorem for finite time blowup”, Nonlinear Analysis-Theory Methods & Applications, 74:17 (2011), 6105–6115
-
Gazzola F., Pavani R., “Blow up oscillating solutions to some nonlinear fourth order differential equations”, Nonlinear Analysis-Theory Methods & Applications, 74:17 (2011), 6696–6711
-
Lan K.Q., Lin W., “A variational inequality index for condensing maps in Hilbert spaces and applications to semilinear elliptic inequalities”, Nonlinear Analysis-Theory Methods & Applications, 74:16 (2011), 5415–5425
-
Fino A.Z., “Critical exponent for damped wave equations with nonlinear memory”, Nonlinear Analysis-Theory Methods & Applications, 74:16 (2011), 5495–5505
-
Zhang Zh., Li Zh., “An optimal Liouville-type theorem of the quasilinear parabolic equation with a p-Laplace operator”, Nonlinear Analysis-Theory Methods & Applications, 74:16 (2011), 5735–5744
-
Kerbal S., “On a recent result of Cazenave, Dickstein and Weissler”, Appl Math Lett, 24:10 (2011), 1693–1697
-
Galaktionov V.A., Mitidieri E., Pohozaev S.I., “Variational approach to complicated similarity solutions of higher-order nonlinear PDEs. II”, Nonlinear Anal Real World Appl, 12:4 (2011), 2435–2466
-
Fino A.Z., Kirane M., “Qualitative properties of solutions to a nonlocal evolution system”, Math Methods Appl Sci, 34:9 (2011), 1125–1143
-
Dzhokhadze O.M., Kharibegashvili S.S., “Some properties and applications of the Riemann and Green-Hadamard functions for linear second-order hyperbolic equations”, Differ Equ, 47:4 (2011), 471–487
-
Похожаев С.И., “Об отсутствии глобальных решений некоторых начально-краевых задач для уравнения Кортевега–де Фриза”, Дифференциальные уравнения, 47:4 (2011), 493–498
; Pokhozhaev S.I., “On the nonexistence of global solutions of some initial-boundary value problems for the Korteweg-de Vries equation”, Differ Equ, 47:4 (2011), 488–493 -
Похожаев С.И., “О существовании и отсутствии решений некоторых квазилинейных гиперболических уравнений”, Дифференциальные уравнения, 47:12 (2011), 1732–1732
; Pokhozhaev S.I., “On the Existence and Nonexistence of Solutions of Some Quasilinear Hyperbolic Equations”, Differ Equ, 47:12 (2011), 1754–1762 -
Ю. В. Мухартова, А. А. Панин, “О разрушении решения одной неоднородной системы уравнений типа С. Л. Соболева”, Матем. заметки, 91:2 (2012), 225–239
; Yu. V. Mukhartova, A. A. Panin, “Blow-Up of the Solution of an Inhomogeneous System of Sobolev-Type Equations”, Math. Notes, 91:2 (2012), 217–230 -
М. О. Корпусов, “О разрушении решений трехмерного уравнения Розенау–Бюргерса”, ТМФ, 170:3 (2012), 342–349
; M. O. Korpusov, “Blowup of solutions of the three-dimensional Rosenau–Burgers equation”, Theoret. and Math. Phys., 170:3 (2012), 280–286 -
М. О. Корпусов, “О разрушении ионно-звуковых волн в плазме с нелинейными источниками на границе”, Изв. РАН. Сер. матем., 76:2 (2012), 103–140
; M. O. Korpusov, “Blow-up of ion-sound waves in plasma with non-linear sources on the boundary”, Izv. Math., 76:2 (2012), 310–345 -
М. О. Корпусов, “О разрушении решений модельных волновых уравнений с положительной энергией в нелинейной механике”, ТМФ, 171:1 (2012), 3–17
; M. O. Korpusov, “Blowup of a positive-energy solution of model wave equations in nonlinear dynamics”, Theoret. and Math. Phys., 171:1 (2012), 421–434 -
Ю. В. Мухартова, А. А. Панин, “О разрушении решения одной неоднородной системы уравнений соболевского типа”, Изв. РАН. Сер. матем., 76:3 (2012), 157–182
; Yu. V. Mukhartova, A. A. Panin, “Blow-up of solutions of an inhomogeneous system of Sobolev-type equations”, Izv. Math., 76:3 (2012), 581–606 -
Fino A.Z., Kirane M., “Qualitative Properties of Solutions to a Time-Space Fractional Evolution Equation”, Quart Appl Math, 70:1 (2012), 133–157
-
Fino A.Z., Jazar M., “Blow-up solutions of second-order differential inequalities with a nonlinear memory term”, Nonlinear Analysis-Theory Methods & Applications, 75:6 (2012), 3122–3129
-
Kalamajska A., Pietruska-Paluba K., Skrzypczak I., “Nonexistence Results for Differential Inequalities Involving a-Laplacian”, Advances in Differential Equations, 17:3–4 (2012), 307–336
-
Liu Ch., “Critical exponent for a quasilinear parabolic equation with inhomogeneous density in a cone”, Monatsh Math, 165:2 (2012), 237–249
-
Kon'kov A.A., “On comparison theorems for elliptic inequalities”, J Math Anal Appl, 388:1 (2012), 102–124
-
Li X., Li F., “Nonexistence of solutions for singular quasilinear differential inequalities with a gradient nonlinearity”, Nonlinear Analysis-Theory Methods & Applications, 75:5 (2012), 2812–2822
-
Fazly M., “Liouville Type Theorems for Stable Solutions of Certain Elliptic Systems”, Adv Nonlinear Stud, 12:1 (2012), 1–17
-
Korpusov M.O., “On the blow-up of solutions of the Benjamin-Bona-Mahony-Burgers and Rosenau-Burgers equations”, Nonlinear Analysis-Theory Methods & Applications, 75:4 (2012), 1737–1743
-
Quoc Hung Phan, Souplet Ph., “Liouville-type theorems and bounds of solutions of Hardy-Henon equations”, J Differential Equations, 252:3 (2012), 2544–2562
-
Berchio E., Farina A., Ferrero A., Gazzola F., “Existence and stability of entire solutions to a semilinear fourth order elliptic problem”, J Differential Equations, 252:3 (2012), 2596–2616
-
Aliev A.B., Kazimov A.A., “Existence, non-existence and asymptotic behavior of global solutions to the Cauchy problem for systems of semilinear hyperbolic equations with damping terms”, Nonlinear Analysis-Theory Methods & Applications, 75:1 (2012), 91–102
-
Zhang Zh., Li Zh., “A universal bound for radial solutions of the quasilinear parabolic equation with p-Laplace operator”, J Math Anal Appl, 385:1 (2012), 125–134
-
Е. В. Юшков, “О разрушении решения уравнения, родственного уравнению Кортевега–де Фриза”, ТМФ, 172:1 (2012), 64–72
; E. V. Yushkov, “Blowup of solutions of a Korteweg–de Vries-type equation”, Theoret. and Math. Phys., 172:1 (2012), 932–938 -
Коньков А.А., “О свойствах решений нелинейных эллиптических неравенств, содержащих члены с младшими производными”, Доклады Академии наук, 442:3 (2012), 306–306
; Kon'kov A.A., “On the properties of solutions of nonlinear elliptic inequalities containing terms with lower order derivatives”, Doklady Mathematics, 85:1 (2012), 51–54 -
Корпусов М.О., “О разрушении решения уравнения с градиентной нелинейностью”, Дифференциальные уравнения, 48:6 (2012), 790–790
; Korpusov M.O., “On the Blow-Up of the Solution of an Equation with a Gradient Nonlinearity”, Differ. Equ., 48:6 (2012), 796–808 -
Похожаев С.И., “Отсутствие глобальных знакопеременных решений нелинейного уравнения теплопроводности”, Доклады Академии наук, 443:3 (2012), 296–296
; Pohozaev S.I., “Blow-Up of Global Sign-Changing Solutions of a Nonlinear Heat Equation”, Dokl. Math., 85:2 (2012), 225–228 -
Похожаев С.И., “Об одном классе начально-краевых задач для уравнений типа кортевегаде фриза”, Дифференциальные уравнения, 48:3 (2012), 368–368
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Е. И. Галахов, “Об одной модели нелинейного рассеяния”, Матем. заметки, 92:3 (2012), 368–380
; E. I. Galakhov, “On a Nonlinear Scattering Model”, Math. Notes, 92:3 (2012), 333–344 -
М. О. Корпусов, “О разрушении решений волнового диссипативного уравнения типа Кирхгоффа с источником и с положительной энергией”, Сиб. матем. журн., 53:4 (2012), 874–891
; M. O. Korpusov, “On blowup of solutions to a Kirchhoff type dissipative wave equation with a source and positive energy”, Siberian Math. J., 53:4 (2012), 702–717 -
М. О. Корпусов, “Разрушение решений уравнения теплопроводности с двойной нелинейностью”, ТМФ, 172:3 (2012), 339–343
; M. O. Korpusov, “Solution blowup for the heat equation with double nonlinearity”, Theoret. and Math. Phys., 172:3 (2012), 1173–1176 -
Е. В. Юшков, “О разрушении решения в системах типа Кортвега–де Фриза”, ТМФ, 173:2 (2012), 197–206
; E. V. Yushkov, “Blowup in Korteweg–de Vries-type systems”, Theoret. and Math. Phys., 173:2 (2012), 1498–1506 -
Е. В. Юшков, “О разрушении решений задач гидродинамического типа с сингулярным источником”, Ж. вычисл. матем. и матем. физ., 52:8 (2012), 1523–1535
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С. И. Похожаев, “Об отсутствии глобальных решений задачи Коши для уравнения Кортевега–де Фриза”, Функц. анализ и его прил., 46:4 (2012), 51–60
; S. I. Pokhozhaev, “On the Nonexistence of Global Solutions of the Cauchy Problem for the Korteweg–de Vries Equation”, Funct. Anal. Appl., 46:4 (2012), 279–286 -
D'Ambrosio L., Mitidieri E., “A Priori Estimates and Reduction Principles for Quasilinear Elliptic Problems and Applications”, Adv. Differ. Equat., 17:9-10 (2012), 935–1000
-
Wang W., Hong L., “Liouville-Type Theorems for Semilinear Elliptic Systems”, Nonlinear Anal.-Theory Methods Appl., 75:13 (2012), 5380–5391
-
Pohozaev S.I., “Blow-Up of Smooth Solutions of the Korteweg-de Vries Equation”, Nonlinear Anal.-Theory Methods Appl., 75:12 (2012), 4688–4698
-
Quoc Hung Phan, “Liouville-Type Theorems and Bounds of Solutions for Hardy-Henon Elliptic Systems”, Adv. Differ. Equat., 17:7-8 (2012), 605–634
-
Sun F. Shi P., “Global Existence and Non-Existence for a Higher-Order Parabolic Equation with Time-Fractional Term”, Nonlinear Anal.-Theory Methods Appl., 75:10 (2012), 4145–4155
-
Li X. Li F., “Nonexistence of Solutions for Nonlinear Differential Inequalities with Gradient Nonlinearities”, Commun. Pure Appl. Anal, 11:3 (2012), 935–943
-
Kharibegashvili S., Midodashvili B., “Solvability of Nonlocal Problems for Semilinear One-Dimensional Wave Equations”, Electron. J. Differ. Equ., 2012, 28
-
Quittner P., Souplet Ph., “Symmetry of Components for Semilinear Elliptic Systems”, SIAM J. Math. Anal., 44:4 (2012), 2545–2559
-
Qassim M.D., Furati K.M., Tatar N.-E., “On a Differential Equation Involving Hilfer-Hadamard Fractional Derivative”, Abstract Appl. Anal., 2012, 391062
-
Манита О.А., Шапошников С.В., “Нелинейные параболические уравнения для мер”, Доклады академии наук, 447:6 (2012), 610–610
; Manita O.A., Shaposhnikov S.V., “Nonlinear Parabolic Equations for Measures”, Dokl. Math., 86:3 (2012), 857–860 -
Юшков Е.В., “О разрушении решений уравнений гидродинамического типа при специальных граничных условиях”, Дифференциальные уравнения, 48:9 (2012), 1234–1234
; Yushkov E.V., “On the Blow-Up of Solutions of Equations of Hydrodynamic Type Under Special Boundary Conditions”, Differ. Equ., 48:9 (2012), 1212–1218 -
Дж. О. Огун, Ю. Н. Орлов, В. Ж. Сакбаев, “О преобразовании пространства начальных данных для задачи Коши с особенностями решения типа взрыва”, Препринты ИПМ им. М. В. Келдыша, 2012, 087, 31 с.
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М. О. Корпусов, “О разрушении решения уравнения, родственного уравнению Гамильтона–Якоби”, Матем. заметки, 93:1 (2013), 81–95
; M. O. Korpusov, “On the Blow-Up of the Solution of an Equation Related to the Hamilton–Jacobi Equation”, Math. Notes, 93:1 (2013), 90–101 -
Э. И. Абдурагимов, “Единственность положительного радиально-симметричного решения задачи Дирихле для одной нелинейной эллиптической системы второго порядка”, Матем. заметки, 93:1 (2013), 3–12
; E. I. Abduragimov, “Uniqueness of Positive Radially Symmetric Solutions of the Dirichlet Problem for a Nonlinear Elliptic System of Second Order”, Math. Notes, 93:1 (2013), 3–11 -
М. О. Корпусов, “О разрушении решений класса параболических уравнений с двойной нелинейностью”, Матем. сб., 204:3 (2013), 19–42
; M. O. Korpusov, “Solution blow-up for a class of parabolic equations with double nonlinearity”, Sb. Math., 204:3 (2013), 323–346 -
М. О. Корпусов, “Разрушение решений обобщенного уравнения Клейна–Гордона с сильной диссипацией”, Изв. РАН. Сер. матем., 77:2 (2013), 109–138
; M. O. Korpusov, “Blow-up of solutions of strongly dissipative generalized Klein–Gordon equations”, Izv. Math., 77:2 (2013), 325–353 -
М. О. Корпусов, “Разрушение решений нелинейных уравнений и систем нелинейных уравнений теории волн”, ТМФ, 174:3 (2013), 355–363
; M. O. Korpusov, “Blowup of solutions of nonlinear equations and systems of nonlinear equations in wave theory”, Theoret. and Math. Phys., 174:3 (2013), 307–314 -
В. Ж. Сакбаев, “Разрушение решений задачи Коши для нелинейного уравнений Шрëдингера”, Вестн. Сам. гос. техн. ун-та. Сер. Физ.-мат. науки, 1(30) (2013), 159–171
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Kharibegashvili S., Midodashvili B., “On the Solvability of One Boundary Value Problem for One Class of Semilinear Second Order Hyperbolic Systems”, J. Math. Anal. Appl., 400:2 (2013), 345–362
-
Lei Yu., “Asymptotic Properties of Positive Solutions of the Hardy-Sobolev Type Equations”, J. Differ. Equ., 254:4 (2013), 1774–1799
-
D'Ambrosio L., “A New Critical Curve for a Class of Quasilinear Elliptic Systems”, Nonlinear Anal.-Theory Methods Appl., 78 (2013), 62–78
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Алиев А.Б., Казимов А.А., “Глобальная разрешимость задачи коши для полулинейных гиперболических уравнений с диссипацией и анизотропной эллиптической частью”, Доклады академии наук, 448:3 (2013), 255–255
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Корпусов М.О., “О разрушении решений одной диссипативной системы уравнений с положительной энергией в классической теории поля”, Дифференциальные уравнения, 49:3 (2013), 310–310
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Алиев А.Б., Казимов А.А., “Глобальная разрешимость и поведение решений задачи Коши для систем двух полулинейных гиперболических уравнений с диссипацией”, Дифференциальные уравнения, 49:4 (2013), 476–476
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Похожаев С.И., “Отсутствие глобальных решений нелинейных эволюционных уравнений”, Дифференциальные уравнения, 49:5 (2013), 625–625
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Е. И. Галахов, “Принципы сравнения для оператора $p$-Лапласа”, Труды Шестой Международной конференции по дифференциальным и функционально-дифференциальным уравнениям (Москва, 14–21 августа, 2011). Часть 4, СМФН, 48, РУДН, М., 2013, 27–35
; E. I. Galakhov, “Comparison principles for the $p$-Laplacian operator”, Journal of Mathematical Sciences, 202:6 (2014), 825–834 -
А. Б. Муравник, “О разрушении решений некоторых систем квазилинейных параболических неравенств”, Труды Шестой Международной конференции по дифференциальным и функционально-дифференциальным уравнениям (Москва, 14–21 августа, 2011). Часть 4, СМФН, 48, РУДН, М., 2013, 84–92
; A. B. Muravnik, “On blow-up of solutions of some systems of quasilinear parabolic inequalities”, Journal of Mathematical Sciences, 202:6 (2014), 859–868 -
С. С. Харибегашвили, О. М. Джохадзе, “Задача Коши–Гурса для волновых уравнений с нелинейным диссипативным членом”, Матем. заметки, 94:6 (2013), 889–907
; S. S. Kharibegashvili, O. M. Dzhokhadze, “The Cauchy–Goursat Problem for Wave Equations with Nonlinear Dissipative Term”, Math. Notes, 94:6 (2013), 913–929 -
А. А. Панин, “Локальная разрешимость и разрушение решения для уравнения Розенау–Бюргерса с различными граничными условиями”, ТМФ, 177:1 (2013), 93–110
; A. A. Panin, “Local solvability and blowup of the solution of the Rosenau–Bürgers equation with different boundary conditions”, Theoret. and Math. Phys., 177:1 (2013), 1361–1376 -
М. О. Корпусов, Е. В. Юшков, “Разрушение решений систем уравнений мелкой воды”, ТМФ, 177:2 (2013), 264–275
; M. O. Korpusov, E. V. Yushkov, “Solution blowup for systems of shallow-water equations”, Theoret. and Math. Phys., 177:2 (2013), 1505–1514 -
В. Ж. Сакбаев, “Градиентный взрыв решений задачи Коши для уравнения Шрëдингера”, Теория функций и уравнения математической физики, Сборник статей. К 90-летию со дня рождения члена-корреспондента РАН Льва Дмитриевича Кудрявцева, Тр. МИАН, 283, МАИК «Наука/Интерпериодика», М., 2013, 171–187
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Е. И. Галахов, “О некоторых неравенствах в частных производных с градиентными слагаемыми”, Теория функций и уравнения математической физики, Сборник статей. К 90-летию со дня рождения члена-корреспондента РАН Льва Дмитриевича Кудрявцева, Тр. МИАН, 283, МАИК «Наука/Интерпериодика», М., 2013, 40–48
; E. I. Galakhov, “On some partial differential inequalities with gradient terms”, Proc. Steklov Inst. Math., 283 (2013), 35–43 -
Lorenzo D'Ambrosio, Enzo Mitidieri, “Entire solutions of quasilinear elliptic systems on Carnot groups”, Теория функций и уравнения математической физики, Сборник статей. К 90-летию со дня рождения члена-корреспондента РАН Льва Дмитриевича Кудрявцева, Тр. МИАН, 283, МАИК «Наука/Интерпериодика», М., 2013, 9–24
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С. С. Харибегашвили, О. М. Джохадзе, “Задача Коши–Дарбу для одномерного волнового уравнения со степенной нелинейностью”, Сиб. матем. журн., 54:6 (2013), 1407–1426
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Amorim P. Antontsev S., “Young Measure Solutions for the Wave Equation with P(X, T)-Laplacian: Existence and Blow-Up”, Nonlinear Anal.-Theory Methods Appl., 92 (2013), 153–167
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И. В. Асташова, “О равномерных оценках решений нелинейного дифференциального уравнения третьего порядка”, Тр. сем. им. И. Г. Петровского, 29, Изд-во Моск. ун-та, М., 2013, 146–161
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А. А. Коньков, “О стабилизации решений нелинейного уравнения Фоккера–Планка”, Тр. сем. им. И. Г. Петровского, 29, Изд-во Моск. ун-та, М., 2013, 333–345
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С. С. Харибегашвили, О. М. Джохадзе, “О глобальных и взрывных решениях смешанной задачи с нелинейным граничным условием для одномерного полулинейного волнового уравнения”, Матем. сб., 205:4 (2014), 121–148
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М. О. Корпусов, А. Г. Свешников, Е. В. Юшков, “Разрушение решений нелинейных уравнений типа Кадомцева–Петвиашвили и Захарова–Кузнецова”, Изв. РАН. Сер. матем., 78:3 (2014), 79–110
; M. O. Korpusov, A. G. Sveshnikov, E. V. Yushkov, “Blow-up of solutions of non-linear equations of Kadomtsev–Petviashvili and Zakharov–Kuznetsov types”, Izv. Math., 78:3 (2014), 500–530 -
А. А. Коньков, “О теоремах сравнения для квазилинейных эллиптических неравенств, учитывающих геометрию области”, Изв. РАН. Сер. матем., 78:4 (2014), 123–174
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D'Ambrosio L. Mitidieri E., “Hardy-Littlewood-Sobolev Systems and Related Liouville Theorems”, Discret. Contin. Dyn. Syst.-Ser. S, 7:4 (2014), 653–671
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Sun Yu., “Uniqueness Result for Non-Negative Solutions of Semi-Linear Inequalities on Riemannian Manifolds”, J. Math. Anal. Appl., 419:1 (2014), 643–661
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Grigor'yan A. Sun Yu., “On Nonnegative Solutions of the Inequality Delta U Plus U(SIGMA) <= 0 on Riemannian Manifolds”, Commun. Pure Appl. Math., 67:8 (2014), 1336–1352
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Galaktionov V.A., Mitidieri E., Pohozaev S.I., “Classification of Global and Blow-Up Sign-Changing Solutions of a Semilinear Heat Equation in the Subcritical Fujita Range : Second-Order Diffusion”, Adv. Nonlinear Stud., 14:1 (2014), 1–29
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М. О. Корпусов, А. А. Панин, “О разрушении решения абстрактной задачи Коши для формально гиперболического уравнения с двойной нелинейностью”, Изв. РАН. Сер. матем., 78:5 (2014), 91–142
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Aliev A.B., Kazimov A.A., “the Existence and Nonexistence of Global Solutions of the Cauchy Problem For Klein-Gordon Systems”, Dokl. Math., 90:3 (2014), 680–682
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Min L.-H., “Liouville Type Theorem For Higher Order Hardy-Henon System of Inequalities”, Math. Inequal. Appl., 17:4 (2014), 1427–1439
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Cowan C., “a Liouville Theorem For a Fourth Order Henon Equation”, Adv. Nonlinear Stud., 14:3 (2014), 767–776
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Montaru A., Sirakov B., Souplet Ph., “Proportionality of Components, Liouville Theorems and a Priori Estimates For Noncooperative Elliptic Systems”, Arch. Ration. Mech. Anal., 213:1 (2014), 129–169
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Fazly M., Ghoussoub N., “on the Henon-Lane-Emden Conjecture”, Discret. Contin. Dyn. Syst., 34:6, SI (2014), 2513–2533
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Liu Ch., “the Critical Fujita Exponent For a Diffusion Equation With a Potential Term”, Lith. Math. J., 54:2 (2014), 182–191
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Montaru A., Souplet Ph., “Symmetry of Components and Liouville Theorems For Noncooperative Elliptic Systems on the Half-Space”, C. R. Math., 352:4 (2014), 321–325
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Korpusov M.O., Yushkov E.V., “Local Solvability and Blow-Up For Benjamin-Bona-Mahony-Burgers, Rosenau-Burgers and Korteweg-de Vries-Benjamin-Bona-Mahony Equations”, Electron. J. Differ. Equ., 2014, 69
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Galakhov E., Salieva O., Uvarova L., “Blow-Up of Solutions To Systems of Nonlinear Inequalities With Singularities on Unbounded Sets”, Electron. J. Differ. Equ., 2014, 216
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Khomrutai S., Kitisin N., “Blow-Up in Non-Autonomous Semilinear Pseudoparabolic Equations”, Scienceasia, 40:5 (2014), 371–374
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Kirane M., Ahmad B., Alsaedi A., Al-Yami M., “Non-Existence of Global Solutions To a System of Fractional Diffusion Equations”, Acta Appl. Math., 133:1 (2014), 235–248
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Lupo D., Payne K.R., Popivanov N.I., “on the Degenerate Hyperbolic Goursat Problem For Linear and Nonlinear Equations of Tricomi Type”, Nonlinear Anal.-Theory Methods Appl., 108 (2014), 29–56
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Nishihara K., Wakasugi Yu., “Critical Exponent For the Cauchy Problem To the Weakly Coupled Damped Wave System”, Nonlinear Anal.-Theory Methods Appl., 108 (2014), 249–259
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D'Ambrosio L., Dipierro S., “Hardy Inequalities on Riemannian Manifolds and Applications”, Ann. Inst. Henri Poincare-Anal. Non Lineaire, 31:3 (2014), 449–475
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D'Ambrosio L., Mitidieri E., “Liouville Theorems For Elliptic Systems and Applications”, J. Math. Anal. Appl., 413:1 (2014), 121–138
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Yang JinGe, Cao Yang, Zheng SiNing, “Fujita Phenomena in Nonlinear Pseudo-Parabolic System”, Sci. China-Math., 57:3 (2014), 555–568
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Fang Zh.B., Xu L., “Liouville Theorems For a Singular Parabolic Differential Inequality With a Gradient Term”, J. Inequal. Appl., 2014, 62
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O. Jokhadze, “The Cauchy problem for one-dimensional wave equations with a nonlinear dissipative term”, Eurasian Math. J., 5:4 (2014), 92–112
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Б. Тсегау, “Об отсутствии глобальных решений для квазилинейных обратных параболических неравенств с оператором типа $p$-Лапласа”, Матем. заметки, 97:4 (2015), 591–603
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Ghergu M., Taliaferro S.D., “Nonexistence of Positive Supersolutions of Nonlinear Biharmonic Equations Without the Maximum Principle”, Commun. Partial Differ. Equ., 40:6 (2015), 1029–1069
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А. А. Панин, “О локальной разрешимости и разрушении решения абстрактного нелинейного интегрального уравнения Вольтерра”, Матем. заметки, 97:6 (2015), 884–903
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S. G. Pyatkov, S. N. Shergin, “On some mathematical models of filtration theory”, Вестн. ЮУрГУ. Сер. Матем. моделирование и программирование, 8:2 (2015), 105–116
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Е. И. Галахов, О. А. Салиева, “Разрушение решений некоторых нелинейных неравенств с особенностями на неограниченных множествах”, Матем. заметки, 98:2 (2015), 187–195
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Е. В. Юшков, М. О. Корпусов, “Глобальная неразрешимость одномерных задач для уравнений типа Бюргерса”, Матем. заметки, 98:3 (2015), 448–462
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М. О. Корпусов, “Критические показатели мгновенного разрушения или локальной разрешимости нелинейных уравнений соболевского типа”, Изв. РАН. Сер. матем., 79:5 (2015), 103–162
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Л. С. Ефремова, В. Ж. Сакбаев, “Понятие взрыва множества решений дифференциальных уравнений и усреднение случайных полугрупп”, ТМФ, 185:2 (2015), 252–271
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Nabti A., “Nonexistence of Non-Trivial Global Weak Solutions For Higher-Order Nonlinear Schrodinger Equations”, Electron. J. Differ. Equ., 2015, 312
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Tsegaw B.B., “on the Nonexistence of Solutions of Some Anisotropic Elliptic and Backward Parabolic Inequalities”, Differ. Equ., 51:12 (2015), 1607–1619
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Boutefnouchet M., Kirane M., “Nonexistence of Solutions of Some Non-Linear Non-Local Evolution Systems on the Heisenberg Group”, Fract. Calc. Appl. Anal., 18:6 (2015), 1336–1349
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Quoc Hung Phan, Anh Tuan Duong, “Liouville-Type Theorems For a Quasilinear Elliptic Equation of the H,Non-Type”, NoDea-Nonlinear Differ. Equ. Appl., 22:6 (2015), 1817–1829
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Farina A., “Symmetry of Components, Liouville-Type Theorems and Classification Results For Some Nonlinear Elliptic Systems”, Discret. Contin. Dyn. Syst., 35:12, SI (2015), 5869–5877
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Hu L.-G., “Liouville Type Results For Semi-Stable Solutions of the Weighted Lane-Emden System”, J. Math. Anal. Appl., 432:1 (2015), 429–440
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Aliev A.B., Pashayev A.F., “Cauchy Problem For a Class of Fourth-Order Semilinear Pseudohyperbolic Equations With Structural Damping”, Dokl. Math., 92:3 (2015), 651–654
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Cassani D., Tarsi C., “Existence of Solitary Waves For Supercritical Schrodinger Systems in Dimension Two”, Calc. Var. Partial Differ. Equ., 54:2 (2015), 1673–1704
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Albanese G., Mari L., Rigoli M., “on the Role of Gradient Terms in Coercive Quasilinear Differential Inequalities on Carnot Groups”, Nonlinear Anal.-Theory Methods Appl., 126 (2015), 234–261
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Ahmad B., Alsaedi A., Kirane M., “Nonexistence of Global Solutions of Some Nonlinear Space-Nonlocal Evolution Equations on the Heisenberg Group”, Electron. J. Differ. Equ., 2015, 227
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Sun Yu., “on the Uniqueness of Nonnegative Solutions of Differential Inequalities With Gradient Terms on Riemannian Manifolds”, Commun. Pure Appl. Anal, 14:5 (2015), 1743–1757
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Zhang Q.-G., Sun H.-R., “the Blow-Up and Global Existence of Solutions of Cauchy Problems For a Time Fractional Diffusion Equation”, Topol. Methods Nonlinear Anal., 46:1 (2015), 69–92
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Kon'kov A.A., “on Properties of Solutions of Quasilinear Second-Order Elliptic Inequalities”, Nonlinear Anal.-Theory Methods Appl., 123-124 (2015), 89–114
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Huang J.-Ch., “Liouville Type Theorem For Quasi-Linear Elliptic Inequality Delta(P)U + U(SIGMA) <= 0 on Riemannian Manifolds”, J. Math. Anal. Appl., 428:1 (2015), 12–31
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Yang J., “Fujita-Type Phenomenon of Nonlinear Coupled Nonlocal Diffusion System”, J. Math. Anal. Appl., 428:1 (2015), 227–237
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Sun Yu., “on Nonexistence of Positive Solutions of Quasi-Linear Inequality on Riemannian Manifolds”, Proc. Amer. Math. Soc., 143:7 (2015), PII S0002-9939(2015)12705-0, 2969–2984
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Farina A., “Some Symmetry Results and Liouville-Type Theorems For Solutions To Semilinear Equations”, Nonlinear Anal.-Theory Methods Appl., 121 (2015), 223–229
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Bordoni S. Filippucci R. Pucci P., “Nonlinear Elliptic Inequalities With Gradient Terms on the Heisenberg Group”, Nonlinear Anal.-Theory Methods Appl., 121 (2015), 262–279
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Khomrutai S., “Global and Blow-Up Solutions of Superlinear Pseudoparabolic Equations With Unbounded Coefficient”, Nonlinear Anal.-Theory Methods Appl., 122 (2015), 192–214
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Azman I. Jleli M. Samet B., “Blow-Up of Solutions To Parabolic Inequalities in the Heisenberg Group”, Electron. J. Differ. Equ., 2015, 167
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Alves C.O., Santos C.A., Zhou J., “Existence and Non-Existence of Blow-Up Solutions For a Non-Autonomous Problem With Indefinite and Gradient Terms”, Z. Angew. Math. Phys., 66:3 (2015), 891–918
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Galakhov E., Salieva O., Uvarova L., “Nonexistence Results For Some Nonlinear Elliptic and Parabolic Inequalities With Functional Parameters”, Electron. J. Qual. Theory Differ., 2015, no. 85, UNSP 85, 1–11
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Li X., “Nonexistence of Solutions For Singular Nonlinear Ordinary Inequalities”, Electron. J. Qual. Theory Differ., 2015, no. 67
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Deviaterikova E., Galakhov E., Salieva O., Uvarova L., “Blow-Up Time For a Problem of Heat Transfer With Coefficients Depending on Their Formation Mechanisms”, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics 2014 (Icnaam-2014), AIP Conference Proceedings, 1648, eds. Simos T., Tsitouras C., Amer Inst Physics, 2015, UNSP 750003
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Galakhov E., Salieva O., “on Blow-Up For a Generalized Heat Inequality”, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics 2014 (Icnaam-2014), AIP Conference Proceedings, 1648, eds. Simos T., Tsitouras C., Amer Inst Physics, 2015, UNSP 750004
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Aliev A.B., Kazimov A.A., “Nonexistence of global solutions of the Cauchy problem for systems of Klein–Gordon equations with positive initial energy”, Differ. Equ., 51:12 (2015), 1563–1568
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Kharibegashvili S.S., Dzhokhadze O.M., “Time-periodic problem for a weakly nonlinear telegraph equation with directional derivative in the boundary condition”, Differ. Equ., 51:10 (2015), 1369–1386
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Ching J., Cirstea F., “Existence and classification of singular solutions to nonlinear elliptic equations with a gradient term”, Anal. PDE, 8:8 (2015), 1931–1962
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А. А. Коньков, “Об оценках решений эллиптических неравенств в окрестности особой точки”, Матем. заметки, 99:4 (2016), 623–625
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Abdelmalek S., Bajneed M., Sioud Kh., “Nonexistence of Solutions To Cauchy Problems For Fractional Time Semi-Linear Pseudo-Hyperbolic Systems”, Electron. J. Differ. Equ., 2016, 20
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Sun Yu., “Uniqueness Result on Nonnegative Solutions of a Large Class of Differential Inequalities on Riemannian Manifolds”, Pac. J. Math., 280:1 (2016), 241–254
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Villavert J., “Asymptotic and Optimal Liouville Properties For Wolff Type Integral Systems”, Nonlinear Anal.-Theory Methods Appl., 130 (2016), 102–120
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М. О. Корпусов, “О разрушении за конечное время решения начально-краевой задачи для нелинейного уравнения ионно-звуковых волн”, ТМФ, 187:3 (2016), 447–454
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С. С. Харибегашвили, О. М. Джохадзе, “О разрешимости периодической задачи для одного нелинейного телеграфного уравнения”, Сиб. матем. журн., 57:4 (2016), 940–950
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Li J., Yin J., Jin Ch., “Strong solutions of a class of fully nonlinear degenerate parabolic equations”, Math. Meth. Appl. Sci., 39:8 (2016), 2025–2037
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