Positive solutions for some non-autonomous Schrodinger-Poisson systems

In this paper we study the Schrodinger-Poisson system {-Delta u + u + K(x)phi(x)u = a(x)|u|(p-1)u, x is an element of R-3, (SP) -Delta phi = K(x)u(2), x is an element of R-3, with p is an element of (3, 5). Assuming that a: R-3 -> R and K: R-3 -> R are non-negative functions such that lim(|x| -> infinity) a(x) = a(infinity) > 0, lim(|x| -> infinity) K(x) = 0 and satisfying suitable assumptions, but not requiring any symmetry property on them, we prove the existence of positive solutions. (C) 2009 Elsevier Inc. All rights reserved.