Annali di Matematica Pura ed Applicata (1923 -)

, Volume 194, Issue 1, pp 43–53

Standing waves with large frequency for 4-superlinear Schrödinger–Poisson systems

Article

DOI: 10.1007/s10231-013-0363-5

Cite this article as:
Chen, H. & Liu, S. Annali di Matematica (2015) 194: 43. doi:10.1007/s10231-013-0363-5

Abstract

We consider standing waves with frequency \(\omega \) for 4-superlinear Schrödinger–Poisson system. For large \(\omega \), the problem reduces to a system of elliptic equations in \(\mathbb R ^3\) with potential indefinite in sign. The variational functional does not satisfy the mountain pass geometry. The nonlinearity considered here satisfies a condition which is much weaker than the classical (AR) condition and the condition (Je) of Jeanjean. We obtain nontrivial solution and, in case of odd nonlinearity, an unbounded sequence of solutions via the local linking theorem and the fountain theorem, respectively.

Keywords

Schrödinger–Poisson systems 4-superlinear \((C)^*\) condition Local linking 

Mathematics Subject Classification (2010)

58E05 35J60 

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsShantou UniversityShantouPeople’s Republic of China
  2. 2.School of Mathematical SciencesXiamen UniversityXiamenPeople’s Republic of China

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