Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations
We study the existence of positive solutions for the boundary value problem of nonlinear fractional differential equations D0+αu(t)+λf(u(t))=0, 0<t<1, u(0)=u(1)=u'(0)=0, where 2<α≤3 is a real number, D0+α is the Riemann-Liouville fractional derivative, λ is a positive parameter, and f:...
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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/10.1155/2011/390543 |
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| _version_ | 1832555428980981760 |
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| author | Yige Zhao Shurong Sun Zhenlai Han Qiuping Li |
| author_facet | Yige Zhao Shurong Sun Zhenlai Han Qiuping Li |
| author_sort | Yige Zhao |
| collection | DOAJ |
| description | We study the existence of positive solutions for the boundary value problem of nonlinear fractional differential equations D0+αu(t)+λf(u(t))=0, 0<t<1, u(0)=u(1)=u'(0)=0, where 2<α≤3 is a real number, D0+α is the Riemann-Liouville fractional derivative, λ is a positive parameter, and f:(0,+∞)→(0,+∞) is continuous. By the properties of the Green function and Guo-Krasnosel'skii fixed point theorem on cones, the eigenvalue intervals of the nonlinear fractional differential equation boundary value problem are considered, some sufficient conditions for the nonexistence and existence of at least one or two positive solutions for the boundary value problem are established. As an application, some examples are presented to illustrate the main results. |
| format | Article |
| id | doaj-art-9632d12b6fec43e6b4f8b89a1a7bc773 |
| 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-9632d12b6fec43e6b4f8b89a1a7bc7732025-02-03T05:48:16ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/390543390543Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential EquationsYige Zhao0Shurong Sun1Zhenlai Han2Qiuping Li3School of Science, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Science, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Science, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Science, University of Jinan, Jinan, Shandong 250022, ChinaWe study the existence of positive solutions for the boundary value problem of nonlinear fractional differential equations D0+αu(t)+λf(u(t))=0, 0<t<1, u(0)=u(1)=u'(0)=0, where 2<α≤3 is a real number, D0+α is the Riemann-Liouville fractional derivative, λ is a positive parameter, and f:(0,+∞)→(0,+∞) is continuous. By the properties of the Green function and Guo-Krasnosel'skii fixed point theorem on cones, the eigenvalue intervals of the nonlinear fractional differential equation boundary value problem are considered, some sufficient conditions for the nonexistence and existence of at least one or two positive solutions for the boundary value problem are established. As an application, some examples are presented to illustrate the main results.http://dx.doi.org/10.1155/2011/390543 |
| spellingShingle | Yige Zhao Shurong Sun Zhenlai Han Qiuping Li Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations Abstract and Applied Analysis |
| title | Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations |
| title_full | Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations |
| title_fullStr | Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations |
| title_full_unstemmed | Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations |
| title_short | Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations |
| title_sort | positive solutions to boundary value problems of nonlinear fractional differential equations |
| url | http://dx.doi.org/10.1155/2011/390543 |
| work_keys_str_mv | AT yigezhao positivesolutionstoboundaryvalueproblemsofnonlinearfractionaldifferentialequations AT shurongsun positivesolutionstoboundaryvalueproblemsofnonlinearfractionaldifferentialequations AT zhenlaihan positivesolutionstoboundaryvalueproblemsofnonlinearfractionaldifferentialequations AT qiupingli positivesolutionstoboundaryvalueproblemsofnonlinearfractionaldifferentialequations |