Solutions of a class of Hamiltonian elliptic systems in

We study the existence of ground state solutions for the following elliptic systems in R N { − Δ u + b ⋅ ∇ x u + u = H v ( x , u , v ) , − Δ v − b ⋅ ∇ x v + v = H u ( x , u , v ) , where b = ( b 1 , … , b N ) is a constant vector and H ∈ C 1 ( R N × R 2 , R ) is nonperiodic in variables x and super-quadratic as | z | → ∞ . By a recent critical point theorem for strongly indefinite problem, we obtain the existence of at least one ground state solution.