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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Hindawi Limited
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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doaj-9779ec13cb5b4199bce5d314b19cef3a2021-07-02T11:57:34ZengHindawi LimitedAdvances 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Wenbo Wang Jianwen Zhou Yongkun Li |
| spellingShingle |
Wenbo Wang Jianwen Zhou Yongkun Li On the Ground State to Hamiltonian Elliptic System with Choquard’s Nonlinear Term Advances in Mathematical Physics |
| author_facet |
Wenbo Wang Jianwen Zhou Yongkun Li |
| author_sort |
Wenbo Wang |
| title |
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_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_sort |
on the ground state to hamiltonian elliptic system with choquard’s nonlinear term |
| publisher |
Hindawi Limited |
| series |
Advances in Mathematical Physics |
| issn |
1687-9120 1687-9139 |
| publishDate |
2020-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/2020/8358629 |
| work_keys_str_mv |
AT wenbowang onthegroundstatetohamiltonianellipticsystemwithchoquardsnonlinearterm AT jianwenzhou onthegroundstatetohamiltonianellipticsystemwithchoquardsnonlinearterm AT yongkunli onthegroundstatetohamiltonianellipticsystemwithchoquardsnonlinearterm |
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1721330557258825728 |