Multiple solutions for Schrodinger-Poisson systems with indefinite potential and combined nonlinearity

In this paper, we study the existence of infinitely many solutions for the following nonlinear Schrodinger-Poisson system {-Delta u + V(x)u + phi u = f(x,u) g(x,u), x is an element of R-3, -Delta phi = u(2), lim(vertical bar x vertical bar ->infinity) phi(x) = 0, where the potential V may be unbounded from below. Under some mild conditions on the nonlinear terms f and g, we obtain infinitely many solutions of this system. Recent results from the literature are generalized and significantly improved. (C) 2017 Elsevier Inc. All rights reserved.