Ground state solutions for the nonlinear Schrodinger-Maxwell equations

In this paper we study the nonlinear Schrodinger-Maxwell equations {-Delta u + V(x)u + phi u = vertical bar u vertical bar(p-1)u in R-3, -Delta phi = u(2) in R-3. If V is a positive constant, we prove the existence of a ground state solution (u, phi) for 2 < p < 5. The non-constant potential case is treated for 3 < p < 5, and V possibly unbounded below. Existence and nonexistence results are proved also when the nonlinearity exhibits a critical growth. (C) 2008 Elsevier Inc. All rights reserved.