Sign-changing solutions for a fractional Schrödinger–Poisson system

Abstract

In this paper, we deal with the existence and multiplicity of sign-changing solutions for fractional Schrödinger–Poisson system: (℘) where , and f is a continuous function. Based on perturbation approach and the method of invariant sets of descending flow, we obtain the existence and multiplicity of sign-changing solutions of system (). In addition, by applying the constrained variational method incorporated with Brouwer degree theory, we prove that system () possesses at least one ground state sign-changing solution. Furthermore, we show that the least energy of sign-changing solutions exceed twice than the least energy, and when f is odd, system () admits infinitely many nontrivial solutions.