Multiplicity of concentrating positive solutions for Schrodinger-Poisson equations with critical growth

被引：25
|
作者：
He, Xiaoming [1 ]
Zou, Wenming [2 ]
机构：
[1] Minzu Univ China, Coll Sci, Beijing 100081, Peoples R China
[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2018年 / 170卷
基金：
中国国家自然科学基金;
关键词：
Schrodinger-Poisson equation; Positive solutions; Ljusternik-Schnirelmann category; Penalization method; ELLIPTIC PROBLEMS; THOMAS-FERMI; BOUND-STATES; WAVES; ATOMS;
D O I：
10.1016/j.na.2018.01.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we deal with a nonlinear Schrodinger-Poisson equation involving critical Sobolev exponent. Under a local condition imposed on the potential, we relate the number of positive solutions with the topology of the set where the potential attains its minimum values. In the proofs we apply Szulkin and Weth's generalized Nehari manifold methods, penalization techniques and Ljusternik-Schnirelmann theory. (c) 2018 Elsevier Ltd. All rights reserved.
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页码：142 / 170
页数：29
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