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

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

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
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
3. A. A. Kon'kov, “On non-negative solutions of quasilinear elliptic inequalities”, Izv. Math., 63:2 (1999), 255–329
4. A. A. Kon'kov, “On solutions of quasilinear elliptic inequalities vanishing in a neighborhood of infinity”, Math. Notes, 67:1 (2000), 122–125
5. Kon'kov A., “Behavior of Solutions of Nonlinear Second-Order Elliptic Inequalities”, Nonlinear Anal.-Theory Methods Appl., 42:7 (2000), 1253–1270
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
7. Kon'kov A., “Nonnegative Solutions of Quasilinear Elliptic Inequalities in Domains Contained in a Layer”, Differ. Equ., 36:7 (2000), 988–997
8. Kon'kov A., “Elliptic Inequalities in Unbounded Plane Domains”, Russ. J. Math. Phys., 7:1 (2000), 119–123
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
10. Laptev, GG, “Nonexistence results for higher-order evolution partial differential inequalities”, Proceedings of the American Mathematical Society, 131:2 (2003), 415
11. A. A. Kon'kov, “Behavior of Solutions of Quasilinear Elliptic Inequalities”, Journal of Mathematical Sciences, 134:3 (2006), 2073–2237
12. Kon'kov A., “Comparison Theorems for Second-Order Elliptic Inequalities”, Nonlinear Anal.-Theory Methods Appl., 59:4 (2004), 583–608
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
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
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