On Hamiltonian elliptic systems with periodic or non-periodic potentials

This paper is concerned with the following Hamiltonian elliptic system{−Δu+b(x)⋅∇u+V(x)u=Hv(x,u,v),−Δv−b(x)⋅∇v+V(x)v=Hu(x,u,v) for x∈RNx∈RN. Existence and multiplicity of solutions are obtained for the systems with periodic or non-periodic potentials V via variational methods.