On the nonlinear Schrodinger-Poisson systems with sign-changing potential

被引：41

作者：

Sun, Juntao ^{[1
]}

Wu, Tsung-fang ^{[2
]}

机构：

[1] Shandong Univ Technol, Sch Sci, Zibo 255049, Peoples R China

[2] Natl Univ Kaohsiung, Dept Appl Math, Kaohsiung 811, Taiwan

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2015年 / 66卷 / 04期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Nonlinear Schrodinger-Poisson systems; Variational methods; Concentration of solutions; GROUND-STATE SOLUTIONS; POSITIVE SOLUTIONS; BOUND-STATES; EXISTENCE; EQUATIONS; MAXWELL; MULTIPLICITY; WAVES;

D O I：

10.1007/s00033-015-0494-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study a nonlinear Schrodinger-Poisson system (-Delta u + V-lambda (x) u + mu K (x) phi u = f (x, u) in R-3,R- -Delta phi = K (x) u(2) in R-3, where is a parameter, is allowed to be sign-changing and f is an indefinite function. We require that with V (+) having a bounded potential well Omega whose depth is controlled by lambda and for all . Under some suitable assumptions on K and f, the existence and the nonexistence of nontrivial solutions are obtained by using variational methods. Furthermore, the phenomenon of concentration of solutions is explored as well.

引用

页码：1649 / 1669

页数：21

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