Existence and multiplicity of solutions for Schr?dinger–Poisson equations with sign-changing potential

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• 作者：Yiwei Ye ; Chun-Lei Tang
• 关键词：35J47 ; 35J50
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2015
• 出版时间：May 2015
• 年：2015
• 卷：53
• 期：1-2
• 页码：383-411
• 全文大小：355 KB
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• 作者单位：Yiwei Ye (1) (2)
  Chun-Lei Tang (1)
  
  1. School of Mathematics and Statistics, Southwest University, Chongqing, ?400715, China
  2. Department of Mathematics, Chongqing Normal University, Chongqing, ?40133, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Systems Theory and Control
  Calculus of Variations and Optimal Control
  Mathematical and Computational Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0835

文摘

In this paper, we study the existence and multiplicity of solutions for the Schr?dinger–Poisson equations $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta u+\lambda V(x)u+K(x)\phi u=f(x,u)\ \ \ \ \ &{} \ \text{ in }\mathbb {R}^3,\\ -\Delta \phi =K(x)u^2\ \ \ \ \ \ &{} \ \text{ in } \mathbb {R}^3, \end{array}\right. \end{aligned}$$