Ground state solutions for superlinear elliptic systems on RNRN

This paper is concerned with the existence of the ground state solutions for the following superlinear elliptic system of Hamiltonian type, {−Δu+V(x)u=g(x,v)in RN,−Δv+V(x)v=f(x,u)in RN,u(x)→0andv(x)→0as |x|→∞, where V∈C(RN,R)V∈C(RN,R) is periodic in x1,x2,…,xNx1,x2,…,xN. We assume that 0 lies in a gap of the spectrum −Δ+V−Δ+V, and ff and gg 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.