Solutions of a class of Hamiltonian elliptic systems in RNRN

We study the existence of ground state solutions for the following elliptic systems in RNRN{−Δu+b⋅∇xu+u=Hv(x,u,v),−Δv−b⋅∇xv+v=Hu(x,u,v), where b=(b1,…,bN)b=(b1,…,bN) is a constant vector and H∈C1(RN×R2,R)H∈C1(RN×R2,R) is nonperiodic in variables x   and super-quadratic as |z|→∞|z|→∞. By a recent critical point theorem for strongly indefinite problem, we obtain the existence of at least one ground state solution.