Positive and sign-changing solutions of a Schrodinger-Poisson system involving a critical nonlinearity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:408

Article

Huang, Lirong¹  Rocha, Eugenio M.¹  Chen, Jianqing¹ 

[1] Univ Aveiro, Dept Math, Ctr Res & Dev Math & Applicat, P-3810193 Aveiro, Portugal

关键词: Schrodinger-Poisson system;    Variational methods;    Critical nonlinearity;    Sign-changing solutions;   

DOI  :  10.1016/j.jmaa.2013.05.071

来源: Elsevier

【 摘 要 】

In this paper, we consider the Schrodinger-Poisson system {-Delta u + u + l(x)phi u = k(x)vertical bar u vertical bar(4)u + mu h(x)u in R-3, -Delta phi = l(x)u(2) in R-3, where mu is a positive constant and the nonlinear growth of vertical bar u vertical bar(4)u reaches the Sobolev critical exponent since 2* = 6 for three spatial dimensions. We prove the existence of at least a pair of fixed sign solutions and a pair of sign-changing Solutions in H-1(R-3) x D-1,D-2(R-3) under some suitable conditions on the nonnegative functions I, k and h, but not requiring any symmetry properties on them. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free