Eigenvalue of Fractional Differential Equations with p-Laplacian Operator
We investigate the existence of positive solutions for the fractional order eigenvalue problem with p-Laplacian operator -𝒟tβ(φp(𝒟tαx))(t)=λf(t,x(t)), t∈(0,1), x(0)=0, 𝒟tαx(0)=0, 𝒟tγx(1)=∑j=1m-2aj𝒟tγx(ξj), where 𝒟tβ, 𝒟tα, 𝒟tγ are the standard Riemann-Liouville derivatives and p-Laplacian oper...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/137890 |
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| author | Wenquan Wu Xiangbing Zhou |
| author_facet | Wenquan Wu Xiangbing Zhou |
| author_sort | Wenquan Wu |
| collection | DOAJ |
| description | We investigate the existence of positive solutions for the fractional order eigenvalue problem with p-Laplacian operator -𝒟tβ(φp(𝒟tαx))(t)=λf(t,x(t)), t∈(0,1), x(0)=0, 𝒟tαx(0)=0, 𝒟tγx(1)=∑j=1m-2aj𝒟tγx(ξj), where 𝒟tβ, 𝒟tα, 𝒟tγ are the standard Riemann-Liouville derivatives and p-Laplacian operator is defined as φp(s)=|s|p-2s, p>1.f:(0,1)×(0,+∞)→[0,+∞) is continuous and f can be singular at t=0,1 and x=0. By constructing upper and lower solutions, the existence of positive solutions for the eigenvalue problem of fractional differential equation is established. |
| format | Article |
| id | doaj-art-96b2b2f826c442a287ba4191b0b9ce51 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-96b2b2f826c442a287ba4191b0b9ce512025-02-03T01:22:21ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/137890137890Eigenvalue of Fractional Differential Equations with p-Laplacian OperatorWenquan Wu0Xiangbing Zhou1Department of Mathematics, Aba Teachers College, Wenchuan, Sichuan 623002, ChinaDepartment of Mathematics, Aba Teachers College, Wenchuan, Sichuan 623002, ChinaWe investigate the existence of positive solutions for the fractional order eigenvalue problem with p-Laplacian operator -𝒟tβ(φp(𝒟tαx))(t)=λf(t,x(t)), t∈(0,1), x(0)=0, 𝒟tαx(0)=0, 𝒟tγx(1)=∑j=1m-2aj𝒟tγx(ξj), where 𝒟tβ, 𝒟tα, 𝒟tγ are the standard Riemann-Liouville derivatives and p-Laplacian operator is defined as φp(s)=|s|p-2s, p>1.f:(0,1)×(0,+∞)→[0,+∞) is continuous and f can be singular at t=0,1 and x=0. By constructing upper and lower solutions, the existence of positive solutions for the eigenvalue problem of fractional differential equation is established.http://dx.doi.org/10.1155/2013/137890 |
| spellingShingle | Wenquan Wu Xiangbing Zhou Eigenvalue of Fractional Differential Equations with p-Laplacian Operator Discrete Dynamics in Nature and Society |
| title | Eigenvalue of Fractional Differential Equations with p-Laplacian Operator |
| title_full | Eigenvalue of Fractional Differential Equations with p-Laplacian Operator |
| title_fullStr | Eigenvalue of Fractional Differential Equations with p-Laplacian Operator |
| title_full_unstemmed | Eigenvalue of Fractional Differential Equations with p-Laplacian Operator |
| title_short | Eigenvalue of Fractional Differential Equations with p-Laplacian Operator |
| title_sort | eigenvalue of fractional differential equations with p laplacian operator |
| url | http://dx.doi.org/10.1155/2013/137890 |
| work_keys_str_mv | AT wenquanwu eigenvalueoffractionaldifferentialequationswithplaplacianoperator AT xiangbingzhou eigenvalueoffractionaldifferentialequationswithplaplacianoperator |