Upper and Lower Solutions Method for a Class of Singular Fractional Boundary Value Problems with p-Laplacian Operator
The upper and lower solutions method is used to study the p-Laplacian fractional boundary value problem D0+γ(ϕp(D0+αu(t)))=f(t,u(t)), 0<t<1, u(0)=0, u(1)=au(ξ), D0+αu(0)=0, and D0+αu(1)=bD0+αu(η), where 1<α,γ⩽2,0⩽a,b⩽1,0<ξ,η<1. Some new results on the existence of at least one positiv...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/971824 |
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| _version_ | 1832548369023631360 |
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| author | Jinhua Wang Hongjun Xiang |
| author_facet | Jinhua Wang Hongjun Xiang |
| author_sort | Jinhua Wang |
| collection | DOAJ |
| description | The upper and lower solutions method is used to study the p-Laplacian fractional boundary value problem D0+γ(ϕp(D0+αu(t)))=f(t,u(t)), 0<t<1, u(0)=0, u(1)=au(ξ), D0+αu(0)=0, and D0+αu(1)=bD0+αu(η), where 1<α,γ⩽2,0⩽a,b⩽1,0<ξ,η<1. Some new results on the existence of at least one positive solution are obtained. It is valuable to point out that the nonlinearity f can be singular at t=0,1 or u=0. |
| format | Article |
| id | doaj-art-ee2c6ddbda674a778c7490280a302dbb |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ee2c6ddbda674a778c7490280a302dbb2025-02-03T06:14:17ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/971824971824Upper and Lower Solutions Method for a Class of Singular Fractional Boundary Value Problems with p-Laplacian OperatorJinhua Wang0Hongjun Xiang1Department of Mathematics, Xiangnan University, Chenzhou 423000, ChinaDepartment of Mathematics, Xiangnan University, Chenzhou 423000, ChinaThe upper and lower solutions method is used to study the p-Laplacian fractional boundary value problem D0+γ(ϕp(D0+αu(t)))=f(t,u(t)), 0<t<1, u(0)=0, u(1)=au(ξ), D0+αu(0)=0, and D0+αu(1)=bD0+αu(η), where 1<α,γ⩽2,0⩽a,b⩽1,0<ξ,η<1. Some new results on the existence of at least one positive solution are obtained. It is valuable to point out that the nonlinearity f can be singular at t=0,1 or u=0.http://dx.doi.org/10.1155/2010/971824 |
| spellingShingle | Jinhua Wang Hongjun Xiang Upper and Lower Solutions Method for a Class of Singular Fractional Boundary Value Problems with p-Laplacian Operator Abstract and Applied Analysis |
| title | Upper and Lower Solutions Method for a Class of Singular Fractional Boundary Value Problems with p-Laplacian Operator |
| title_full | Upper and Lower Solutions Method for a Class of Singular Fractional Boundary Value Problems with p-Laplacian Operator |
| title_fullStr | Upper and Lower Solutions Method for a Class of Singular Fractional Boundary Value Problems with p-Laplacian Operator |
| title_full_unstemmed | Upper and Lower Solutions Method for a Class of Singular Fractional Boundary Value Problems with p-Laplacian Operator |
| title_short | Upper and Lower Solutions Method for a Class of Singular Fractional Boundary Value Problems with p-Laplacian Operator |
| title_sort | upper and lower solutions method for a class of singular fractional boundary value problems with p laplacian operator |
| url | http://dx.doi.org/10.1155/2010/971824 |
| work_keys_str_mv | AT jinhuawang upperandlowersolutionsmethodforaclassofsingularfractionalboundaryvalueproblemswithplaplacianoperator AT hongjunxiang upperandlowersolutionsmethodforaclassofsingularfractionalboundaryvalueproblemswithplaplacianoperator |