Multiple solutions for Schrodinger-Poisson systems with indefinite potential and combined nonlinearity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Zhang, Qingye¹  Xu, Bin² 

[1] Jiangxi Normal Univ, Dept Math, Nanchang 880022, Jiangxi, Peoples R China

[2] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China

关键词: Schrodinger-Poisson system;    Symmetric mountain pass lemma;    Variational method;   

DOI  :  10.1016/j.jmaa.2017.06.058

来源: Elsevier

【 摘 要 】

In this paper, we study the existence of infinitely many solutions for the following nonlinear Schrodinger-Poisson system {-Delta u + V(x)u + phi u = f(x,u) g(x,u), x is an element of R-3, -Delta phi = u(2), lim(vertical bar x vertical bar ->infinity) phi(x) = 0, where the potential V may be unbounded from below. Under some mild conditions on the nonlinear terms f and g, we obtain infinitely many solutions of this system. Recent results from the literature are generalized and significantly improved. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free