Existence and Multiplicity of Solutions for a Fractional Schrodinger-Poisson System with Subcritical or Critical Growth

In this paper, we study the existence of positive ground state solutions and infinitely many geometrically distinct solutions for the following fractional Schrodinger- Poisson system {(-delta)(s )u + V (x)u + phi u = f (x, u), in R-3, (-delta)(s )phi = u(2), in R-3, where s is an element of (3/4, 1) is a fixed constant, f is continuous, superlinear at infinity with subcritical or critical growth and V and f are asymptotically periodic in x. Applying the method of Nehari manifold and Lusternik-Schnirelmann category theory, three existence results are given.