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Mat. Zametki, 1996, Volume 60, Issue 1, Pages 30–39 (Mi mz1801)  

This article is cited in 4 scientific papers (total in 4 papers)

Behavior at infinity of solutions of second-order nonlinear equations of a particular class

A. A. Kon'kov

N. E. Bauman Moscow State Technical University

Abstract: Let $\Omega$ be an arbitrary, possibly unbounded, open subset of $\mathbb R^n$, and let $L$ be an elliptic operator of the form
$$ L=\sum_{i,j=1}^n \frac\partial{\partial x_i} (a_{ij}(x)\frac\partial{\partial x_j}). $$
The behavior at infinity of the solutions of the equation $Lu=f(|u|)\operatorname{sign}u$ in $\Omega$ is studied, where $f$ is a measurable function. In particular, given certain conditions at infinity, the uniqueness theorem for the solution of the first boundary value problem is proved.

DOI: https://doi.org/10.4213/mzm1801

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English version:
Mathematical Notes, 1996, 60:1, 22–28

Bibliographic databases:

UDC: 517
Received: 15.02.1994

Citation: A. A. Kon'kov, “Behavior at infinity of solutions of second-order nonlinear equations of a particular class”, Mat. Zametki, 60:1 (1996), 30–39; Math. Notes, 60:1 (1996), 22–28

Citation in format AMSBIB
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\by A.~A.~Kon'kov
\paper Behavior at infinity of solutions of second-order nonlinear equations of a~particular class
\jour Mat. Zametki
\yr 1996
\vol 60
\issue 1
\pages 30--39
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\crossref{https://doi.org/10.4213/mzm1801}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1431457}
\zmath{https://zbmath.org/?q=an:0898.35014}
\transl
\jour Math. Notes
\yr 1996
\vol 60
\issue 1
\pages 22--28
\crossref{https://doi.org/10.1007/BF02308876}
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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. 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
    2. Mamedov, FI, “On local and global properties of solutions of semilinear equations with principal part of the type of a degenerating p-Laplacian”, Differential Equations, 43:12 (2007), 1724  crossref  mathscinet  zmath  isi  scopus
    3. Sh. G. Bagyrov, K. A. Gulieva, “Blow-Up of Positive Solutions of a Second-Order Semilinear Elliptic Equation with Lower Derivatives and with Singular Potential”, Math. Notes, 101:2 (2017), 374–378  mathnet  crossref  crossref  mathscinet  isi  elib
    4. Sh. G. Bagyrov, “Nonexistence of Solutions of a Semilinear Biharmonic Equation with Singular Potential”, Math. Notes, 103:1 (2018), 24–32  mathnet  crossref  crossref  isi  elib
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