On the Ground State to Hamiltonian Elliptic System with Choquard’s Nonlinear Term

الملخص EN

In the present paper, we consider the following Hamiltonian elliptic system with Choquard’s nonlinear term −Δu+Vxu=∫ΩGvy/x−yβdygv in Ω,−Δv+Vxv=∫ΩFuy/x−yαdyfu in Ω,u=0,v=0 on ∂Ω,where Ω⊂ℝN is a bounded domain with a smooth boundary, 0<α

By establishing a strongly indefinite variational setting, we prove that the above problem has a ground state solution.