Existence of solutions for Schrödinger-Poisson system with asymptotically periodic terms

Abstract

In this paper, we consider the following nonlinear Schrödinger-Poisson system { −∆u+ V(x)u+K(x)φu = f(x,u), x ∈ R3, −∆φ = K(x)u2, x ∈ R3, where V ,K ∈ L∞(R3) and f : R3 ×R→ R is continuous. We prove that the problem has a nontrivial solution under asymptotically periodic case of V ,K, and f at infinity. Moreover, the nonlinear term f does not satisfy any monotone condition.