Solutions of a class of Hamiltonian elliptic systems in RN

We study the existence of ground state solutions for the following elliptic systems in R-N {-Delta u + b . del(x)u + u = H-v (x, u, v), -Delta v - b . del(x)v + v = H-u (x, u, v), where b = (b(1),...,b(N)) is a constant vector and H is an element of C-1(R-N x R-2, R) is nonperiodic in variables x and super-quadratic as vertical bar z vertical bar -> infinity. By a recent critical point theorem for strongly indefinite problem, we obtain the existence of at least one ground state solution. (C) 2009 Elsevier Inc. All rights reserved.