Nontrivial solutions for a class of Hamiltonian elliptic system with gradient term

Abstract In this paper we study the following nonlinear Hamiltonian elliptic system with gradient term − Δ u + b → ( x ) ⋅ ∇ u + V ( x ) u = H v ( x , u , v ) i n R N , − Δ v − b → ( x ) ⋅ ∇ v + V ( x ) v = H u ( x , u , v ) i n R N . Under a local super-quadratic condition on the nonlinearity, we obtain a new existence result of nontrivial solutions by using variational method. Here we do not need the global super-quadratic condition, and in this case our result allows the nonlinearity to be super-quadratic at some domains and asymptotically quadratic at other domains. In the proofs we apply some special techniques to demonstrate the link geometry of the energy functional.