Multiplicity of Positive Solutions for Schrodinger-Poisson Systems with a Critical Nonlinearity in R3

被引：0

作者：

Xie, Weihong ^{[1
]}

Chen, Haibo ^{[1
]}

Shi, Hongxia ^{[2
]}

机构：

[1] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

[2] Hunan First Normal Univ, Sch Math & Computat Sci, Changsha 410205, Hunan, Peoples R China

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2019年 / 42卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Multiple positive solutions; Schrodinger-Poisson systems; Variational methods; Barycenter map; Critical Sobolev exponent; NONTRIVIAL SOLUTIONS; EXISTENCE; EQUATIONS;

D O I：

10.1007/s40840-018-0623-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is dedicated to studying the multiplicity of positive solutions for the following Schrodinger-Poisson problem - u + u + fu =.Q( x)| u| q-2u + K( x)| u| 4u, in R3, - f = u2, in R3, where 4 < q < 6 or q = 2,. > 0 is a parameter, K( x) and Q( x) satisfy some mild assumptions. With minimax theorems and Ljusternik-Schnirelmann theory, we investigate the relation between the number of positive solutions and the topology of the set where K( x) attains its global maximum for small..

引用

页码：2657 / 2680

页数：24

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