Existence of infinitely many weak solutions to Kirchhoff–Schrödinger–Poisson systems and related models

Abstract

In this article we investigate the existence of infinitely many weak solutions for Kirchhoff–Schrödinger–Poisson systems via the critical point theory. We obtain infinitely many large energy solutions and negative energy solutions of the system with superlinear nonlinearities by using the fountain theorem and the dual fountain theorem, respectively. Moreover, we establish the existence of infinitely many weak solutions of the problem with sublinear nonlinearities by applying the genus theory introduced by Krasnolsel’skii [Topological Methods in the Theory of Nonlinear Integral Equations (The Macmillan Company, New York, 1964)]. In particular, we do not use the classical Ambrosetti–Rabinowitz condition.