Positive Solutions for a Fractional Boundary Value Problem with Changing Sign Nonlinearity
We discuss the existence of positive solutions to the following fractional m-point boundary value problem with changing sign nonlinearity D0+αu(t)+λf(t,u(t))=0,0<t<1,u(0)=0,D0+βu(1)=∑i=1m-2ηiD0+βu(ξi), where λ is a positive parameter, 1<α≤2, 0<β<α-1, 0<ξ1<⋯<ξm-2<1 with ∑i=...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/214042 |
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| _version_ | 1850169812286701568 |
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| author | Yongqing Wang Lishan Liu Yonghong Wu |
| author_facet | Yongqing Wang Lishan Liu Yonghong Wu |
| author_sort | Yongqing Wang |
| collection | DOAJ |
| description | We discuss the existence of positive solutions to the following fractional m-point boundary value problem with changing sign nonlinearity D0+αu(t)+λf(t,u(t))=0,0<t<1,u(0)=0,D0+βu(1)=∑i=1m-2ηiD0+βu(ξi), where λ is a positive parameter, 1<α≤2, 0<β<α-1, 0<ξ1<⋯<ξm-2<1 with ∑i=1m-2ηiξiα-β-1<1, D0+α is the standard Riemann-Liouville derivative, f and may be singular at t=0 and/or t=1 and also may change sign. The work improves and generalizes some previous results. |
| format | Article |
| id | doaj-art-a5a7731ff7394e5191f3436dccb6513a |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a5a7731ff7394e5191f3436dccb6513a2025-08-20T02:20:38ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/214042214042Positive Solutions for a Fractional Boundary Value Problem with Changing Sign NonlinearityYongqing Wang0Lishan Liu1Yonghong Wu2School of Mathematical Sciences, Qufu Normal University, Shandong, Qufu 273165, ChinaSchool of Mathematical Sciences, Qufu Normal University, Shandong, Qufu 273165, ChinaDepartment of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, AustraliaWe discuss the existence of positive solutions to the following fractional m-point boundary value problem with changing sign nonlinearity D0+αu(t)+λf(t,u(t))=0,0<t<1,u(0)=0,D0+βu(1)=∑i=1m-2ηiD0+βu(ξi), where λ is a positive parameter, 1<α≤2, 0<β<α-1, 0<ξ1<⋯<ξm-2<1 with ∑i=1m-2ηiξiα-β-1<1, D0+α is the standard Riemann-Liouville derivative, f and may be singular at t=0 and/or t=1 and also may change sign. The work improves and generalizes some previous results.http://dx.doi.org/10.1155/2012/214042 |
| spellingShingle | Yongqing Wang Lishan Liu Yonghong Wu Positive Solutions for a Fractional Boundary Value Problem with Changing Sign Nonlinearity Abstract and Applied Analysis |
| title | Positive Solutions for a Fractional Boundary Value Problem with Changing Sign Nonlinearity |
| title_full | Positive Solutions for a Fractional Boundary Value Problem with Changing Sign Nonlinearity |
| title_fullStr | Positive Solutions for a Fractional Boundary Value Problem with Changing Sign Nonlinearity |
| title_full_unstemmed | Positive Solutions for a Fractional Boundary Value Problem with Changing Sign Nonlinearity |
| title_short | Positive Solutions for a Fractional Boundary Value Problem with Changing Sign Nonlinearity |
| title_sort | positive solutions for a fractional boundary value problem with changing sign nonlinearity |
| url | http://dx.doi.org/10.1155/2012/214042 |
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