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Tr. Mat. Inst. Steklova, 2001, Volume 232, Pages 248–267 (Mi tm217)  

This article is cited in 21 scientific papers (total in 22 papers)

Nonexistence of Weak Solutions for Some Degenerate and Singular Hyperbolic Problems on $\mathbb R_+^{n+1}$

E. Mitidieria, S. I. Pohozaevb

a Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, Via A. Valerio 12/1, 34127, Trieste, Italia
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Theorems concerning the absence of weak solutions are proved for a wide class of evolution equations and inequalities. This class includes, in particular, the inequalities with degenerate and singular operators of hyperbolic type.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2001, 232, 240–259

Bibliographic databases:

Document Type: Article
UDC: 517
Received in August 2000

Citation: E. Mitidieri, S. I. Pohozaev, “Nonexistence of Weak Solutions for Some Degenerate and Singular Hyperbolic Problems on $\mathbb R_+^{n+1}$”, Function spaces, harmonic analysis, and differential equations, Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii, Tr. Mat. Inst. Steklova, 232, Nauka, MAIK Nauka/Inteperiodika, M., 2001, 248–267; Proc. Steklov Inst. Math., 232 (2001), 240–259

Citation in format AMSBIB
\Bibitem{MitPok01}
\by E.~Mitidieri, S.~I.~Pohozaev
\paper Nonexistence of Weak Solutions for Some Degenerate and Singular Hyperbolic Problems on $\mathbb R_+^{n+1}$
\inbook Function spaces, harmonic analysis, and differential equations
\bookinfo Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii
\serial Tr. Mat. Inst. Steklova
\yr 2001
\vol 232
\pages 248--267
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm217}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1851453}
\zmath{https://zbmath.org/?q=an:1032.35138}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2001
\vol 232
\pages 240--259


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. G. Laptev, “On the Absence of Solutions for a Class of Singular Semilinear Differential Inequalities”, Proc. Steklov Inst. Math., 232 (2001), 216–228  mathnet  mathscinet  zmath
    2. E. Mitidieri, S. I. Pokhozhaev, “A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities”, Proc. Steklov Inst. Math., 234 (2001), 1–362  mathnet  mathscinet  zmath
    3. D'Ambrosio L., “Critical degenerate inequalities on the Heisenberg group”, Manuscripta Math., 106:4 (2001), 519–536  crossref  mathscinet  zmath  isi
    4. J. Hay, “On Necessary Conditions for the Existence of Local Solutions to Singular Nonlinear Ordinary Differential Equations and Inequalities”, Math. Notes, 72:6 (2002), 847–857  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Laptev G.G., “Nonexistence of solutions for parabolic inequalities in unbounded cone-like domains via the test function method”, J. Evol. Equ., 2:4 (2002), 459–470  crossref  mathscinet  zmath  isi
    6. Hay J., “Necessary conditions for the existence of global solutions of higher–order nonlinear ordinary differential inequalities”, Differ. Equ., 38:3 (2002), 362–368  mathnet  crossref  mathscinet  zmath  isi
    7. Laptev G.G., “Absence of solutions of evolution-type differential inequalities in the exterior of a ball”, Russ. J. Math. Phys., 9:2 (2002), 180–187  mathscinet  zmath  isi
    8. G. G. Laptev, “Non-existence of global solutions for higher-order evolution inequalities in unbounded cone-like domains”, Mosc. Math. J., 3:1 (2003), 63–84  mathnet  mathscinet  zmath
    9. D'Ambrosio L., Lucente S., “Nonlinear Liouville theorems for Grushin and Tricomi operators”, J. Differential Equations, 193:2 (2003), 511–541  crossref  mathscinet  zmath  isi
    10. Hay J., “Necessary conditions for the existence of local solutions to higher-order singular nonlinear ordinary differential equations and inequalities”, Dokl. Math., 67:1 (2003), 66–69  mathnet  mathscinet  zmath  isi
    11. Lupo D., Payne K.R., “Critical exponents for semilinear equations of mixed elliptic-hyperbolic and degenerate types”, Comm. Pure Appl. Math., 56:3 (2003), 403–424  crossref  mathscinet  zmath  isi
    12. Pohozaev S., “The general blow-up for nonlinear PDE's”, Function Spaces, Differential Operators and Nonlinear Analysis: the Hans Triebel Anniversary Volume, 2003, 141–159  crossref  mathscinet  zmath  isi
    13. Caristi G., “Nonexistence of global solutions of higher order evolution inequalities in R-N”, Nonlinear Equations: Methods, Models and Applications, Progress in Nonlinear Differential Equations and their Applications, 54, 2003, 91–105  mathscinet  zmath  isi
    14. El Hamidi A., Laptev G.G., “Nonexistence of solutions to semilinear inequalities in conical domains”, Bull. Belg. Math. Soc. Simon Stevin, 11:3 (2004), 343–364  mathscinet  zmath  isi
    15. El Hamidi A., Laptev G.G., “Existence and nonexistence results for higher-order semilinear evolution inequalities with critical potential”, J. Math. Anal. Appl., 304:2 (2005), 451–463  crossref  mathscinet  zmath  adsnasa  isi  elib
    16. Kaikina E.I., Naumkin P.I., Shishmarev I.A., “On the asymptotic behavior of solutions to the Cauchy problem for a nonlinear Sobolev-type equation”, Dokl. Math., 71:2 (2005), 269–273  mathscinet  zmath  isi  elib
    17. O. V. Besov, A. M. Il'in, V. A. Il'in, L. D. Kudryavtsev, S. M. Nikol'skii, L. V. Ovsyannikov, E. Mitidieri, A. Tesei, L. Véron, “Stanislav Ivanovich Pokhozhaev (on his 70th birthday)”, Russian Math. Surveys, 61:2 (2006), 373–378  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. 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  crossref  mathscinet  zmath  isi
    19. M. Kirane, N.-e. Tatar, “Nonexistence for the Laplace equation with a dynamical boundary condition of fractional type”, Siberian Math. J., 48:5 (2007), 849–856  mathnet  crossref  mathscinet  zmath  isi
    20. Galaktionov V.A., Mitidieri E., Pohozaev S.I., “Capacity induced by a nonlinear operator and applications”, Georgian Math. J., 15:3 (2008), 501–516  mathscinet  zmath  isi
    21. 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  crossref  mathscinet  zmath  isi
    22. D'Abbicco M., Ebert M.R., “A new phenomenon in the critical exponent for structurally damped semi-linear evolution equations”, Nonlinear Anal.-Theory Methods Appl., 149 (2017), 1–40  crossref  mathscinet  zmath  isi  scopus
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