Ground State Solutions to a Critical Nonlocal Integrodifferential System
Consider the following nonlocal integrodifferential system: LKu+λ1u+μ1u2⁎-2u+Gu(x,u,v)=0 in Ω, LKv+λ2v+μ2v2⁎-2v+Gv(x,u,v)=0 in Ω, u=0, v=0 in RN∖Ω, where LK is a general nonlocal integrodifferential operator, λ1,λ2,μ1,μ2>0, 2⁎≔2N/N-2s is a fractional Sobolev critical exponent, 0<s<...
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/4312083 |
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| author | Min Liu Zhijing Wang Zhenyu Guo |
| author_facet | Min Liu Zhijing Wang Zhenyu Guo |
| author_sort | Min Liu |
| collection | DOAJ |
| description | Consider the following nonlocal integrodifferential system: LKu+λ1u+μ1u2⁎-2u+Gu(x,u,v)=0 in Ω, LKv+λ2v+μ2v2⁎-2v+Gv(x,u,v)=0 in Ω, u=0, v=0 in RN∖Ω, where LK is a general nonlocal integrodifferential operator, λ1,λ2,μ1,μ2>0, 2⁎≔2N/N-2s is a fractional Sobolev critical exponent, 0<s<1, N>2s, G(x,u,v) is a lower order perturbation of the critical coupling term, and Ω is an open bounded domain in RN with Lipschitz boundary. Under proper conditions, we establish an existence result of the ground state solution to the nonlocal integrodifferential system. |
| format | Article |
| id | doaj-art-07e087a47f334aaeaa2ab5f4535be4c1 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-07e087a47f334aaeaa2ab5f4535be4c12025-02-03T01:03:41ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/43120834312083Ground State Solutions to a Critical Nonlocal Integrodifferential SystemMin Liu0Zhijing Wang1Zhenyu Guo2School of Sciences, Liaoning Shihua University, Fushun 113001, ChinaSchool of Sciences, Liaoning Shihua University, Fushun 113001, ChinaSchool of Mathematics, Liaoning Normal University, Dalian 116029, ChinaConsider the following nonlocal integrodifferential system: LKu+λ1u+μ1u2⁎-2u+Gu(x,u,v)=0 in Ω, LKv+λ2v+μ2v2⁎-2v+Gv(x,u,v)=0 in Ω, u=0, v=0 in RN∖Ω, where LK is a general nonlocal integrodifferential operator, λ1,λ2,μ1,μ2>0, 2⁎≔2N/N-2s is a fractional Sobolev critical exponent, 0<s<1, N>2s, G(x,u,v) is a lower order perturbation of the critical coupling term, and Ω is an open bounded domain in RN with Lipschitz boundary. Under proper conditions, we establish an existence result of the ground state solution to the nonlocal integrodifferential system.http://dx.doi.org/10.1155/2018/4312083 |
| spellingShingle | Min Liu Zhijing Wang Zhenyu Guo Ground State Solutions to a Critical Nonlocal Integrodifferential System Advances in Mathematical Physics |
| title | Ground State Solutions to a Critical Nonlocal Integrodifferential System |
| title_full | Ground State Solutions to a Critical Nonlocal Integrodifferential System |
| title_fullStr | Ground State Solutions to a Critical Nonlocal Integrodifferential System |
| title_full_unstemmed | Ground State Solutions to a Critical Nonlocal Integrodifferential System |
| title_short | Ground State Solutions to a Critical Nonlocal Integrodifferential System |
| title_sort | ground state solutions to a critical nonlocal integrodifferential system |
| url | http://dx.doi.org/10.1155/2018/4312083 |
| work_keys_str_mv | AT minliu groundstatesolutionstoacriticalnonlocalintegrodifferentialsystem AT zhijingwang groundstatesolutionstoacriticalnonlocalintegrodifferentialsystem AT zhenyuguo groundstatesolutionstoacriticalnonlocalintegrodifferentialsystem |