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Mat. Sb., 1994, Volume 185, Number 9, Pages 81–94 (Mi msb925)  

This article is cited in 14 scientific papers (total in 14 papers)

On properties of solutions of a class of nonlinear second-order equations

V. A. Kondrat'ev, A. A. Kon'kov


Abstract: The boundary value problem
$$ Lu=f(|u|) \quad \text {in}\quad \Omega , \qquad u|_{\partial \Omega }=w, $$
is studied, where $\Omega$ is an arbitrary, possibly unbounded, open subset of $R^n$, $L=\sum\limits_{i,j=1}^n\dfrac \partial {\partial x_i} (a_{ij}(x)\dfrac \partial {\partial x_j})$ is a differential operator of elliptic type with measurable coefficients, and $w$, $f$ are some functions.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1995, 83:1, 67–77

Bibliographic databases:

UDC: 517.9
MSC: 35J65
Received: 27.10.1993

Citation: V. A. Kondrat'ev, A. A. Kon'kov, “On properties of solutions of a class of nonlinear second-order equations”, Mat. Sb., 185:9 (1994), 81–94; Russian Acad. Sci. Sb. Math., 83:1 (1995), 67–77

Citation in format AMSBIB
\Bibitem{KonKon94}
\by V.~A.~Kondrat'ev, A.~A.~Kon'kov
\paper On properties of solutions of a~class of nonlinear second-order equations
\jour Mat. Sb.
\yr 1994
\vol 185
\issue 9
\pages 81--94
\mathnet{http://mi.mathnet.ru/msb925}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1305756}
\zmath{https://zbmath.org/?q=an:0847.35040}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 83
\issue 1
\pages 67--77
\crossref{https://doi.org/10.1070/SM1995v083n01ABEH003580}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995TQ10000003}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kon'kov A., “Positive Solutions of Nonlinear Second-Order Elliptic Inequalities in Unbounded Domains”, Russ. J. Math. Phys., 5:1 (1997), 119–122  mathscinet  isi
    2. A. A. Kon'kov, “Behavior of solutions of quasilinear elliptic inequalities containing terms with lower-order derivatives”, Math. Notes, 64:6 (1998), 817–821  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. A. A. Kon'kov, “On non-negative solutions of quasilinear elliptic inequalities”, Izv. Math., 63:2 (1999), 255–329  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. A. A. Kon'kov, “On solutions of quasilinear elliptic inequalities vanishing in a neighborhood of infinity”, Math. Notes, 67:1 (2000), 122–125  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Kon'kov A., “Behavior of Solutions of Nonlinear Second-Order Elliptic Inequalities”, Nonlinear Anal.-Theory Methods Appl., 42:7 (2000), 1253–1270  crossref  mathscinet  isi
    6. Kon'kov A., “On Nonnegative Solutions of Quasi-Linear Elliptic Inequalities in Domains Belonging to R-2”, Russ. J. Math. Phys., 7:4 (2000), 371–401  mathscinet  isi
    7. Kon'kov A., “Nonnegative Solutions of Quasilinear Elliptic Inequalities in Domains Contained in a Layer”, Differ. Equ., 36:7 (2000), 988–997  mathnet  crossref  mathscinet  isi
    8. Kon'kov A., “Elliptic Inequalities in Unbounded Plane Domains”, Russ. J. Math. Phys., 7:1 (2000), 119–123  mathscinet  isi
    9. 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
    10. Laptev, GG, “Nonexistence results for higher-order evolution partial differential inequalities”, Proceedings of the American Mathematical Society, 131:2 (2003), 415  crossref  mathscinet  zmath  isi  elib
    11. 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
    12. Kon'kov A., “Comparison Theorems for Second-Order Elliptic Inequalities”, Nonlinear Anal.-Theory Methods Appl., 59:4 (2004), 583–608  crossref  mathscinet  isi
    13. Mamedov F.I., Amanov R.A., “On Local and Global Properties of Solutions of Semilinear Equations with Principal Part of the Type of a Degenerating P-Laplacian”, Differ. Equ., 43:12 (2007), 1724–1732  crossref  mathscinet  zmath  isi
    14. Kon'kov A.A., “Solutions of Elliptic Inequalities That Vanish in a Neighborhood of Infinity”, Russ. J. Math. Phys., 19:1 (2012), 131–133  crossref  mathscinet  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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