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...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2015-06, Vol.426 (2), p.839-854
Main Authors: Shen, Zupei, Han, Zhiqing
Format: Article
Language:English
Subjects:
Concentration–compactness principle
Indefinite weight
Nehari manifold
Schrödinger–Poisson system
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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