On ground states for the Schrödinger-Poisson system with periodic potentials

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• 作者：Wen Zhang ; Jian Zhang ; Xiaoliang Xie
• 关键词：Key wordsSchrödinger ; Poisson system ; ground state solutions ; variational methods ; strongly indefinite functionals
• 刊名：Indian Journal of Pure and Applied Mathematics
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：47
• 期：3
• 页码：449-470
• 全文大小：203 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Applications of Mathematics
  Mathematics
  Numerical Analysis
  
• 出版者：Springer India
• ISSN：0975-7465
• 卷排序：47

文摘

This paper is concerned with the following Schrödinger-Poisson system $$\left\{ {\begin{array}{*{20}{c}}{ - \Delta u + V\left( x \right)u - K\left( x \right)\phi \left( x \right)u = q\left( x \right){{\left| u \right|}^{p - 2}}u,}&{in\;{\mathbb{R}^3},} \\ { - \Delta \phi = K\left( x \right){u^2},}&{in\;{\mathbb{R}^3},} \end{array}} \right.$$ where p ∈ (2, 6), V(x) ∈ C(ℝ^{3, ℝ) is a general periodic function, K(x) and q(x) are nonperiodic functions. Under suitable assumptions, we prove the existence of ground state solutions via variational methods for strongly indefinite problems.Key wordsSchrödinger-Poisson systemground state solutionsvariational methodsstrongly indefinite functionalsThis work is partially supported by the NNSF (Nos. 11571370, 11471137, 11471278, 61472136).}