Existence of infinitely many solutions for a class of Schrödinger–Poisson equations without any growth and Ambrosetti–Rabinowitz conditions in

Abstract

In this paper, we study the following kind of Schrödinger–Poisson equations without any growth and Ambrosetti–Rabinowitz conditions: where , is a potential function and satisfies certain conditions. By using variational method, truncation function and Fountain Theorem, we get the existence of infinitely many solutions to revised equations. Then we use the Moser iteration to obtain the existence of infinitely many solutions to original Schrödinger–Poisson equations.