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In the present paper, we consider the following Hamiltonian elliptic system HES: -Δu+bx·∇u+Vxu=Hvx,u,v, x∈RN, -Δv-bx·∇v+Vxv=Hux,u,v, x∈RN. A new existence result of nontrivial solutions is obtained for the system HES via variational methods for strongly indefinite problems, which generalizes some known results in the literatures.

Solutions for a Class of Nonperiodic Superquadratic Hamiltonian Elliptic Systems Involving Gradient Terms