On the Ground State to Hamiltonian Elliptic System with Choquard’s Nonlinear Term
On the Ground State to Hamiltonian Elliptic System with Choquard’s Nonlinear Term
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DOI：
10.1155/2020/8358629
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发表时间：
2020-05
影响因子：
1.2
通讯作者：
Wenbo Wang;Jianwen Zhou;Yongkun Li
中科院分区：
文献类型：
--
作者：
Wenbo Wang;Jianwen Zhou;Yongkun Li
本文考虑具有Choquard非线性项的Hamilton椭圆方程组-Δu+Vxu=<$ΩGvy/x−yβdygv in Ω，-Δv+ Vxu =<$ΩFuy/x−yαdyfu in Ω，u=0，v=0 on <$Ω，其中Ω <$<$N是一个有界区域，具有光滑边界，0αN，0βN，F是f的本原，G也是如此.通过建立一个强不定变分环境，我们证明了上述问题存在基态解。
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, 0αN, 0βN, 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.