Multiple solutions for a class of Schrödinger–Poisson system with indefinite nonlinearity

In this article, we investigate the existence and multiplicity of solutions of Schrödinger–Poisson system{−Δu+u+l(x)ϕu=k(x)|u|2u+λh(x)u,x∈R3−Δϕ=l(x)u2,x∈R3 where the potential k(x) allows sign changing. We obtain the existence and multiplicity of solutions for the system, which can be regarded as co...

Full description

Saved in:
Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 426; no. 2; pp. 839 - 854
Main Authors Shen, Zupei, Han, Zhiqing
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.06.2015
Subjects
Concentration–compactness principle
Indefinite weight
Nehari manifold
Schrödinger–Poisson system
Indefinite weight
Nehari manifold
Concentration–compactness principle
Schrödinger–Poisson system
Online AccessGet full text

Cover

More Information
Summary:In this article, we investigate the existence and multiplicity of solutions of Schrödinger–Poisson system{−Δu+u+l(x)ϕu=k(x)|u|2u+λh(x)u,x∈R3−Δϕ=l(x)u2,x∈R3 where the potential k(x) allows sign changing. We obtain the existence and multiplicity of solutions for the system, which can be regarded as complementary work of Huang et al. (2013) [12].
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2015.01.071