JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 卷:417 |
Schrodinger-Poisson system with singular potential | |
Article | |
Jiang, Yongsheng1  Zhou, Huan-Song1  | |
[1] Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China | |
关键词: Elliptic equations; Variational methods; Schrodinger-Poisson equation; Singular potential; Nonnegative Palais-Smale sequence; | |
DOI : 10.1016/j.jmaa.2014.03.034 | |
来源: Elsevier | |
【 摘 要 】
Consider the following Schrodinger-Poisson system (SP) [ -Delta u + V-lambda(x)u + phi(x)u = vertical bar u vertical bar(p-1)u, x = (y, z) is an element of R-2 x R, -Delta phi=u(2), (vertical bar x vertical bar ->+infinity)lim phi(x) = 0, where V-lambda = lambda + 1/vertical bar y vertical bar(alpha) with lambda >= 0, y = (x(1), x(2)) is an element of R-2 and vertical bar y vertical bar = root x(1)(2) + x(2)(2). When alpha is an element of [0, 8) and max{2, 2+alpha/2} < p < 5, the existence and a priori estimate of positive solutions of problem (SP) are established in suitable weighted Sobolev space. Moreover, the asymptotic behavior of the solutions as lambda -> 0 is also discussed. (C) 2014 Elsevier Inc. All rights reserved.
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