On the Ground State to Hamiltonian Elliptic System with Choquard’s Nonlinear Term
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...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/8358629 |
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| author | Wenbo Wang Jianwen Zhou Yongkun Li |
| author_facet | Wenbo Wang Jianwen Zhou Yongkun Li |
| author_sort | Wenbo Wang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-9779ec13cb5b4199bce5d314b19cef3a |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-9779ec13cb5b4199bce5d314b19cef3a2025-02-03T01:01:30ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/83586298358629On the Ground State to Hamiltonian Elliptic System with Choquard’s Nonlinear TermWenbo Wang0Jianwen Zhou1Yongkun Li2School of Mathematics and Statistics, Yunnan University, Kunming, 650500 Yunnan, ChinaSchool of Mathematics and Statistics, Yunnan University, Kunming, 650500 Yunnan, ChinaSchool of Mathematics and Statistics, Yunnan University, Kunming, 650500 Yunnan, ChinaIn 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.http://dx.doi.org/10.1155/2020/8358629 |
| spellingShingle | Wenbo Wang Jianwen Zhou Yongkun Li On the Ground State to Hamiltonian Elliptic System with Choquard’s Nonlinear Term Advances in Mathematical Physics |
| title | On the Ground State to Hamiltonian Elliptic System with Choquard’s Nonlinear Term |
| title_full | On the Ground State to Hamiltonian Elliptic System with Choquard’s Nonlinear Term |
| title_fullStr | On the Ground State to Hamiltonian Elliptic System with Choquard’s Nonlinear Term |
| title_full_unstemmed | On the Ground State to Hamiltonian Elliptic System with Choquard’s Nonlinear Term |
| title_short | On the Ground State to Hamiltonian Elliptic System with Choquard’s Nonlinear Term |
| title_sort | on the ground state to hamiltonian elliptic system with choquard s nonlinear term |
| url | http://dx.doi.org/10.1155/2020/8358629 |
| work_keys_str_mv | AT wenbowang onthegroundstatetohamiltonianellipticsystemwithchoquardsnonlinearterm AT jianwenzhou onthegroundstatetohamiltonianellipticsystemwithchoquardsnonlinearterm AT yongkunli onthegroundstatetohamiltonianellipticsystemwithchoquardsnonlinearterm |