Multiple positive solutions for a Schrodinger-Poisson-Slater system

被引：61
作者：
Siciliano, Gaetano [1 ]
机构：
[1] Univ Granada, Dpto Anal Matemat, E-18071 Granada, Spain
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 365卷 / 01期
关键词：
Schrodinger-Poisson system; Lusternik-Schnirelmann category; Multiplicity result; MAXWELL EQUATIONS; BOUND-STATES; SEMICLASSICAL STATES; ELLIPTIC PROBLEMS; DOMAIN TOPOLOGY; EXISTENCE; EXPONENT;
D O I：
10.1016/j.jmaa.2009.10.061
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we investigate the existence of positive solutions to the following Schrodinger-Poisson-Slater system {-Delta u + u + lambda phi u = vertical bar u vertical bar(p-2)u in Omega, -Delta phi = u(2) in Omega, u = phi = 0 on partial derivative Omega, where Omega is a bounded domain in R-3, lambda is a fixed positive parameter nd p < 2* = 2N/N-2' We prove that if p is "near" the critical Sobolev exponent 2*, then the number of positive solutions is greater then the Lusternik-Schnirelmann category of Omega. (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码：288 / 299
页数：12
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