Infinitely many solutions for a class of sublinear fractional Schrödinger-Poisson systems

Abstract

In this paper, we consider the following nonlinear fractional Schrödinger-Poisson system {(−∆)^su + V (x)u + K(x)φu = a(x)|u|^q−1u, x ∈ R³, (−∆)^tφ = K(x)u², x ∈ R³} where s,t ∈ (0,1) and 4s + 2t ≥ 3,0 < q < 1, and a,K,V ∈ L∞(R³). When a, V both change sign in R³, by applying the symmetric mountain pass theorem, we prove that the problem has infinitely many solutions under appropriate assumptions on a, K, V.