Ground state solutions of Schrodinger-Poisson systems with variable potential and convolution nonlinearity

In the present paper, we consider the following nonlinear Schrodinger Poisson system with convolution nonlinearity: {-Delta u V (x)u + phi u = (I-alpha * F (u)) f (u), x is an element of R-3, -Delta phi = u(2), x is an element of R-3, where alpha is an element of (0,3), I-alpha: R-3 -> R is the Riesz potential, V is an element of C(R-3, [0, infinity)), f is an element of C(lR, R) and F(t) = integral(t)(0) f(s)ds satisfies lim(vertical bar t vertical bar ->infinity)F(t)/vertical bar t vertical bar(sigma) = infinity with sigma = min{2, (6 + alpha)/4}. By using some new analytic techniques and new inequalities, we prove the above system admits a ground state solution under mild assumptions on V and f. In particular, our results cover and improve the existing ones for the Schrodinger-Poisson system which can be considered as the limited problem when alpha -> 0. (C) 2018 Elsevier Inc. All rights reserved.