Existence and concentration of solutions for the Schrodinger-Poisson equations with steep well potential

In this paper we study a system of Schrodinger-Poisson equations {-Delta u + lambda V(x)u + K(x)phi u = vertical bar u vertical bar(p-2)u, in R-3, -Delta phi = K(x)u(2), in R-3, where lambda > 0 is a parameter, 2 < p < 6. Under suitable assumptions on V and K, the existence of nontrivial solution and concentration results are obtained via variational methods. In particular, the potential V is allowed to be sign-changing for the case p is an element of (4, 6). (C) 2013 Elsevier Inc. All rights reserved.