Asymptotically periodic superquadratic Hamiltonian systems

We obtain existence of solutions for the system{−Δu+V(x)u=Fv(x,u,v),x∈RN,−Δv+V(x)v=Fu(x,u,v),x∈RN, where N≥3N≥3, V∈C(RN,(0,∞))V∈C(RN,(0,∞)) is periodic and F∈C1(RN×R2,R)F∈C1(RN×R2,R) is superquadratic at infinity. We consider the case that F is periodic and asymptotically periodic. In the proofs we apply variational techniques.