Existence of Multiple Nontrivial Solutions for a Strongly Indefinite Schrödinger-Poisson System

Abstract

We consider a Schrödinger-Poisson system in ${ℝ}^3$ with a strongly indefinite potential and a general nonlinearity. Its variational functional does not satisfy the global linking geometry. We obtain a nontrivial solution and, in case of odd nonlinearity, infinitely many solutions using the local linking and improved fountain theorems, respectively.