Nonradial large solutions of sublinear elliptic problems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:330

Article

El Mabrouk, Khalifa ; Hansen, Wolfhard

关键词: large solution;    semilinear Dirichlet problem;    Greenian domain;    Green function;   

DOI  :  10.1016/j.jmaa.2006.08.024

来源: Elsevier

【 摘 要 】

Let p be a nonnegative locally bounded function on R-N, N >= 3, and 0 < gamma < 1. Assuming that the oscillation sup(vertical bar x vertical bar=r) p(x) - inf(vertical bar x vertical bar=r) p(x) tends to zero as r -> infinity at a specified rate, it is shown that the equation Delta u = p(x)u(gamma) admits a positive solution in R-N satisfying lim(vertical bar x vertical bar ->infinity) u(x) = infinity if and only if integral(Rn) p(x)/vertical bar x vertical bar(N-2) dx = infinity. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

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