Existence and concentration of solutions for the Schrodinger-Poisson equations with steep well potential

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:255

Article

Zhao, Leiga¹  Liu, Haidong²  Zhao, Fukun³ 

[1] Beijing Univ Chem Technol, Dept Math, Beijing 100029, Peoples R China

[2] Jiaxing Univ, Coll Math Phys & Informat Engn, Jiaxing 314001, Peoples R China

[3] Yunnan Normal Univ, Dept Math, Kunming 650092, Peoples R China

关键词: Schrodinger-Poisson equations;    Sign-changing potential;    Concentration;   

DOI  :  10.1016/j.jde.2013.03.005

来源: Elsevier

【 摘 要 】

In this paper we study a system of Schrodinger-Poisson equations {-Delta u + lambda V(x)u + K(x)phi u = vertical bar u vertical bar(p-2)u, in R-3, -Delta phi = K(x)u(2), in R-3, where lambda > 0 is a parameter, 2 < p < 6. Under suitable assumptions on V and K, the existence of nontrivial solution and concentration results are obtained via variational methods. In particular, the potential V is allowed to be sign-changing for the case p is an element of (4, 6). (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free