Indian Journal of Pure and Applied Mathematics

, Volume 47, Issue 3, pp 449–470 | Cite as

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

  • Wen Zhang
  • Jian Zhang
  • Xiaoliang Xie


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(ℝ3, 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 words

Schrödinger-Poisson system ground state solutions variational methods strongly indefinite functionals 


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Copyright information

© The Indian National Science Academy 2016

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsHunan University of CommerceHunanP. R. China
  2. 2.School of Mathematics and StatisticsCentral South UniversityHunanP. R. China

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