Multiple solutions for the fractional Schrodinger-Poisson system with concave-convex nonlinearities

In this paper, we study the following fractional Schrodinger-Poisson system {(-Delta)(s)u + V(x)u + phi u = f(x, u) + lambda g(x, u) in R-3, (-Delta)(alpha)phi = u(2) in R-3, where lambda is a parameter, s, alpha is an element of (0,1) and 2s + 2 alpha > 3. Under some suitable assumptions on V, f and g, we obtained the multiplicity of solutions for the above system, by applying variational methods and Ekeland's variational principle. Some recent results from the literature are improved and extended.