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

被引：49

作者：

Huang, Lirong ^{[1
]}

Rocha, Eugenio M. ^{[1
]}

Chen, Jianqing ^{[1
]}

机构：

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

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 408卷 / 01期

关键词：

Schrodinger-Poisson system; Variational methods; Critical nonlinearity; Sign-changing solutions; GROUND-STATE SOLUTIONS; CRITICAL SOBOLEV; EQUATION; REGULARITY; WAVES;

D O I：

10.1016/j.jmaa.2013.05.071

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：55 / 69

页数：15

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