Multiplicity of Solutions for Nonlocal Elliptic System of (p,q)-Kirchhoff Type
This paper is concerned with the following nonlocal elliptic system of (p,q)-Kirchhoff type −[M1(∫Ω|∇u|p)]p−1Δpu=λFu(x,u,v), in Ω, −[M2(∫Ω|∇v|q)]q−1Δqv=λFv(x,u,v), in Ω, u=v=0, on ∂Ω. Under bounded condition on M and some novel and periodic condition on F, some new results of the existence of two so...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/526026 |
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| _version_ | 1832568418238201856 |
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| author | Bitao Cheng Xian Wu Jun Liu |
| author_facet | Bitao Cheng Xian Wu Jun Liu |
| author_sort | Bitao Cheng |
| collection | DOAJ |
| description | This paper is concerned with the following nonlocal elliptic system of (p,q)-Kirchhoff
type −[M1(∫Ω|∇u|p)]p−1Δpu=λFu(x,u,v), in Ω, −[M2(∫Ω|∇v|q)]q−1Δqv=λFv(x,u,v), in Ω, u=v=0, on ∂Ω. Under bounded condition on M and some novel and periodic condition on F, some new
results of the existence of two solutions and three solutions of the above mentioned nonlocal elliptic system are obtained by
means of Bonanno's multiple critical points theorems without the Palais-Smale condition
and Ricceri's three critical points theorem, respectively. |
| format | Article |
| id | doaj-art-31b29a532d4b4fdc8fdf56f4bf93c89e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-31b29a532d4b4fdc8fdf56f4bf93c89e2025-02-03T00:59:07ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/526026526026Multiplicity of Solutions for Nonlocal Elliptic System of (p,q)-Kirchhoff TypeBitao Cheng0Xian Wu1Jun Liu2College of Mathematics and Information Science, Qujing Normal University, Qujing, Yunnan 655011, ChinaDepartment of Mathematics, Yunnan Normal University, Kunming, Yunnan 650092, ChinaCollege of Mathematics and Information Science, Qujing Normal University, Qujing, Yunnan 655011, ChinaThis paper is concerned with the following nonlocal elliptic system of (p,q)-Kirchhoff type −[M1(∫Ω|∇u|p)]p−1Δpu=λFu(x,u,v), in Ω, −[M2(∫Ω|∇v|q)]q−1Δqv=λFv(x,u,v), in Ω, u=v=0, on ∂Ω. Under bounded condition on M and some novel and periodic condition on F, some new results of the existence of two solutions and three solutions of the above mentioned nonlocal elliptic system are obtained by means of Bonanno's multiple critical points theorems without the Palais-Smale condition and Ricceri's three critical points theorem, respectively.http://dx.doi.org/10.1155/2011/526026 |
| spellingShingle | Bitao Cheng Xian Wu Jun Liu Multiplicity of Solutions for Nonlocal Elliptic System of (p,q)-Kirchhoff Type Abstract and Applied Analysis |
| title | Multiplicity of Solutions for Nonlocal Elliptic System of (p,q)-Kirchhoff Type |
| title_full | Multiplicity of Solutions for Nonlocal Elliptic System of (p,q)-Kirchhoff Type |
| title_fullStr | Multiplicity of Solutions for Nonlocal Elliptic System of (p,q)-Kirchhoff Type |
| title_full_unstemmed | Multiplicity of Solutions for Nonlocal Elliptic System of (p,q)-Kirchhoff Type |
| title_short | Multiplicity of Solutions for Nonlocal Elliptic System of (p,q)-Kirchhoff Type |
| title_sort | multiplicity of solutions for nonlocal elliptic system of p q kirchhoff type |
| url | http://dx.doi.org/10.1155/2011/526026 |
| work_keys_str_mv | AT bitaocheng multiplicityofsolutionsfornonlocalellipticsystemofpqkirchhofftype AT xianwu multiplicityofsolutionsfornonlocalellipticsystemofpqkirchhofftype AT junliu multiplicityofsolutionsfornonlocalellipticsystemofpqkirchhofftype |