An asymptotically linear Schrodinger-Poisson system on R3

In this paper, we are concerned with the following nonlinear Schrodinger-Poisson equation -Delta u + beta u + lambda phi u = f(x, u)u, x is an element of R-3, -Delta phi = u(2), lim(vertical bar x vertical bar ->infinity) phi(x) = 0, where u, phi : R-3 -> R are positive functions, the parameters beta, lambda > 0, f (x, s) tend to p(x) and q(x) is an element of L-infinity (R-3), respectively, as s -> 0 and s -> +infinity. Under some simple assumptions on f (x, s), we give existence and nonexistence results, depending on the parameters beta and lambda. (C) 2012 Elsevier Ltd. All rights reserved.