Ground state solutions for some Schrodinger-Poisson systems with periodic potentials

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Sun, Jijiang¹  Ma, Shiwang^2,3 

[1] Nanchang Univ, Dept Math, Nanchang 330031, Peoples R China

[2] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

关键词: Schrodinger-Poisson systems;    Ground state;    Nehari manifold;    Critical exponent;   

DOI  :  10.1016/j.jde.2015.09.057

来源: Elsevier

【 摘 要 】

In this paper, we consider the following nonlinear Schrodinger-Poisson system {-Delta u + V(x)u + phi u = f (x, u), in R-3, -Delta phi = u(2) in R-3, where the nonlinearity f is superlinear at infinity with subcritical or critical growth and V is positive, continuous and periodic in x. The existence of ground state solutions, i.e., nontrivial solutions with least possible energy of this system is obtained. Moreover, when V equivalent to 1, we obtain ground state solutions for the above system with a wide class of superlinear nonlinearities by using a new approach. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free