Existence of Positive Solutions for a Kind of Fractional Boundary Value Problems
We are concerned with the following nonlinear three-point fractional boundary value problem: D0+αut+λatft,ut=0, 0<t<1, u0=0, and u1=βuη, where 1<α≤2, 0<β<1, 0<η<1, D0+α is the standard Riemann-Liouville fractional derivative, at>0 is continuous for 0≤t≤1, and f≥0 is continuou...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/602604 |
| Summary: | We are concerned with the following nonlinear three-point fractional boundary value problem: D0+αut+λatft,ut=0, 0<t<1, u0=0, and u1=βuη, where 1<α≤2, 0<β<1, 0<η<1, D0+α is the standard Riemann-Liouville fractional derivative, at>0 is continuous for 0≤t≤1, and f≥0 is continuous on 0,1×0,∞. By using Krasnoesel'skii's fixed-point theorem and the corresponding Green function, we obtain some results for the existence of positive solutions. At the end of this paper, we give an example to illustrate our main results. |
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| ISSN: | 1085-3375 1687-0409 |