Existence of nontrivial solutions for Schrödinger-Poisson system with sign-changing potential

Abstract

In this article, we are interested to consider Schrödinger-Poisson system while the potential function V is indefinite, and the negative space of Schrödinger operator $-\Delta + V$ is finite-dimensional. Different from many other articles, we consider the condition of nonlinearity g(x,t) is weaker than the Ambrosetti-Rabinowitz condition. The Schrödinger-Poisson system has nontrivial solutions, which can be found through the application of the Local linking theorem.