Ground‐state solution of a nonlinear fractional Schrödinger–Poisson system

Abstract

In this paper, we study the nonlinear fractional Schrödinger–Poisson system where (− Δ)s is the fractional Laplacian of order s, , and is a potential function exhibiting a mixed behavior; that is, V is periodic in some directions while tends to a positive constant in other directions. Using the method of Nehari manifold and a concentration compactness argument of P.‐L. Lions, we establish the existence of a signed ground‐state solution for subcritical problem and for critical problem.