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Mat. Zametki, 2004, Volume 76, Issue 6, Pages 918–921 (Mi mz155)  

On the Solution of a Second-Order Nonlinear Equation in the Exterior of a Compact Set

T. S. Khachlaev

M. V. Lomonosov Moscow State University

Abstract: In this paper, we study the behavior of solutions of a semilinear elliptic equation in the exterior of a compact set as $|x|\to\infty$. Such equations were considered by many authors (for example, Kondrat'ev, Landis, Oleinik, Veron, etc.). In the present paper, we study the case in which in the equation contains lower terms. The coefficients of the lower terms are arbitrary bounded measurable functions. It is shown that the solutions of the equation tend to zero as $|x|\to\infty$.

DOI: https://doi.org/10.4213/mzm155

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English version:
Mathematical Notes, 2004, 76:6, 855–858

Bibliographic databases:

UDC: 517.95
Received: 17.02.2004

Citation: T. S. Khachlaev, “On the Solution of a Second-Order Nonlinear Equation in the Exterior of a Compact Set”, Mat. Zametki, 76:6 (2004), 918–921; Math. Notes, 76:6 (2004), 855–858

Citation in format AMSBIB
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