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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 2, Pages 81–126 (Mi izv328)  

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

On solutions of non-autonomous ordinary differential equations

A. A. Kon'kov

N. E. Bauman Moscow State Technical University

Abstract: This paper deals with the solutions of $m$th-order $m\geqslant 1$ differential equations of the form
$$ w^{(m)}=Q(r,w,…,w^{(m-1)}), $$
where $Q$ belongs to the Carathéodory class $K_{\mathrm{loc}}([a,\infty)\times\mathbb R^m)$, $a>0$.

DOI: https://doi.org/10.4213/im328

Full text: PDF file (2869 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2001, 65:2, 285–327

Bibliographic databases:

MSC: 34A12, 34C11, 34A34, 35J15, 35J25, 49L99, 34C10
Received: 21.03.2000

Citation: A. A. Kon'kov, “On solutions of non-autonomous ordinary differential equations”, Izv. RAN. Ser. Mat., 65:2 (2001), 81–126; Izv. Math., 65:2 (2001), 285–327

Citation in format AMSBIB
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\by A.~A.~Kon'kov
\paper On solutions of non-autonomous ordinary differential equations
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 2
\pages 81--126
\mathnet{http://mi.mathnet.ru/izv328}
\crossref{https://doi.org/10.4213/im328}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1842841}
\zmath{https://zbmath.org/?q=an:1052.34011}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 2
\pages 285--327
\crossref{https://doi.org/10.1070/im2001v065n02ABEH000328}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-4344715196}


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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. 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
    2. 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
    3. 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  scopus
    4. A. A. Kon'kov, “Behavior of Solutions of Quasilinear Elliptic Inequalities”, Journal of Mathematical Sciences, 134:3 (2006), 2073–2237  mathnet  crossref  mathscinet  zmath  elib
    5. T. S. Khachlaev, “The asymptotic behaviour of solutions of a semilinear elliptic equation with increasing coefficient in a cylindrical domain”, Russian Math. Surveys, 59:2 (2004), 383–384  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. Kon'kov A.A., “On non-extendable solutions of ordinary differential equations”, J. Math. Anal. Appl., 298:1 (2004), 184–209  crossref  mathscinet  zmath  isi  elib  scopus
    7. Kon'kov A., “On the asymptotic behaviour of solutions of nonlinear parabolic equations”, Proc. Roy. Soc. Edinburgh Sect. A, 136:2 (2006), 365–384  crossref  mathscinet  zmath  isi  elib  scopus
    8. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. I. V. Astashova, “Uniform estimates of positive solutions to quasi-linear differential equations”, J. Math. Sci. (N. Y.), 143:4 (2007), 3198–3204  mathnet  crossref  mathscinet
    10. A. A. Kon'kov, “On properties of solutions of a class of nonlinear ordinary differential equations”, J. Math. Sci. (N. Y.), 143:4 (2007), 3303–3321  mathnet  crossref  mathscinet  elib
    11. I. V. Astashova, “Uniform estimates for positive solutions of quasi-linear ordinary differential equations”, Izv. Math., 72:6 (2008), 1141–1160  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. I. V. Astashova, “Uniform Estimates for Positive Solutions of Higher Order Quasilinear Differential Equations”, Proc. Steklov Inst. Math., 261 (2008), 22–33  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    13. I. V. Astashova, “Uniform estimates of solutions of a nonlinear third-order differential equation”, J. Math. Sci. (N. Y.), 197:2 (2014), 237–247  mathnet  crossref  elib
    14. A. A. Kon'kov, “Stabilization of solutions of the nonlinear Fokker–Planck equation”, J. Math. Sci. (N. Y.), 197:3 (2014), 358–366  mathnet  crossref  elib
    15. A.A.. Kon’kov, “On the behavior of Kneser solutions of nonlinear ordinary differential equations”, Annali di Matematica, 2015  crossref  mathscinet  scopus
    16. I. V. Astashova, “Asymptotic classification of solutions of singular 4th-order Emden–Fowler equations with a constant negative potential”, J. Math. Sci. (N. Y.), 234:4 (2018), 385–396  mathnet  crossref
    17. A. A. Kon'kov, “Maximum principle for nonlinear parabolic equations”, J. Math. Sci. (N. Y.), 234:4 (2018), 423–439  mathnet  crossref
    18. A. A. Kon'kov, “Blow-up of solutions for a class of nondivergence elliptic inequalities”, Comput. Math. Math. Phys., 57:3 (2017), 453–463  mathnet  crossref  crossref  isi  elib
    19. Astashova I.V., “Asymptotic Behavior of Singular Solutions of Emden-Fowler Type Equations”, Differ. Equ., 55:5 (2019), 581–590  crossref  isi
    20. Kon'kov A.A., “On Rapidly Growing Solutions of a Class of Ordinary Differential Equations”, Dokl. Math., 99:2 (2019), 156–159  crossref  isi
    21. Kon'kov A.A., Shishkov A.E., “On Blow-Up Conditions For Solutions of Higher Order Differential Inequalities”, Appl. Anal., 98:9 (2019), 1581–1590  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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