On the Ground State to Hamiltonian Elliptic System with Choquard’s Nonlinear Term
- Wenbo Wang
- Jianwen Zhou
- Yongkun Li
Publication date
January 2020
DOI Publisher
Hindawi Limited Journal
Advances in Mathematical PhysicsAbstract
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<N, 0<β<N, and F is the primitive of f, similarly for G. By establishing a strongly indefinite variational setting, we prove that the above problem has a ground state solution
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