In the present paper, we consider the following Hamiltonian elliptic system (HES): -Δu+b(x)·∇u+V(x)u=Hv(x,u,v),x∈RN, -Δv-b(x)·∇v+V(x)v=Hu(x,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.
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