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=...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/214042 |
| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |