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...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/602604 |
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doaj-344745c9ed304e67b5c81c29da8820d22020-11-24T22:45:56ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/602604602604Existence of Positive Solutions for a Kind of Fractional Boundary Value ProblemsHongjie Liu0Xiao Fu1Liangping Qi2School of Land Science and Technology, China University of Geosciences, Beijing 10083, ChinaSchool of Science, China University of Geosciences, Beijing 10083, ChinaSchool of Science, China University of Geosciences, Beijing 10083, ChinaWe 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.http://dx.doi.org/10.1155/2014/602604 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Hongjie Liu Xiao Fu Liangping Qi |
| spellingShingle |
Hongjie Liu Xiao Fu Liangping Qi Existence of Positive Solutions for a Kind of Fractional Boundary Value Problems Abstract and Applied Analysis |
| author_facet |
Hongjie Liu Xiao Fu Liangping Qi |
| author_sort |
Hongjie Liu |
| title |
Existence of Positive Solutions for a Kind of Fractional Boundary Value Problems |
| title_short |
Existence of Positive Solutions for a Kind of Fractional Boundary Value Problems |
| title_full |
Existence of Positive Solutions for a Kind of Fractional Boundary Value Problems |
| title_fullStr |
Existence of Positive Solutions for a Kind of Fractional Boundary Value Problems |
| title_full_unstemmed |
Existence of Positive Solutions for a Kind of Fractional Boundary Value Problems |
| title_sort |
existence of positive solutions for a kind of fractional boundary value problems |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2014-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/2014/602604 |
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