Ground-state solutions for superquadratic Hamiltonian elliptic systems with gradient terms

In this paper, we study the following Hamiltonian elliptic system with gradient terms: {−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, where V(x)V(x), b(x)b(x), and H(x,u,v)H(x,u,v) are 11-periodic in xx. Under weak superquadratic assumptions for the nonlinearities, we use much more direct methods to prove that all the Cerami sequences for the energy functional are bounded and establish the existence of ground-state solutions for this system.