Ground state solutions for superlinear elliptic systems on

This paper is concerned with the existence of the ground state solutions for the following superlinear elliptic system of Hamiltonian type, { − Δ u + V ( x ) u = g ( x , v ) in  R N , − Δ v + V ( x ) v = f ( x , u ) in  R N , u ( x ) → 0 and v ( x ) → 0 as  | x | → ∞ , where V ∈ C ( R N , R ) is periodic in x 1 , x 2 , … , x N . We assume that 0 lies in a gap of the spectrum − Δ + V , and f and g are both superlinear at 0 and infinity but they have different increasing rates at infinity. By proving all Cerami sequences for the energy functional are bounded, existence of a ground state solution is obtained.