Positive solutions for a class of fractional 3-point boundary value problems at resonance
In this paper, we study the nonlocal fractional differential equation: {Dα0+u(t)+f(t,u(t))=0,0<t<1,u(0)=0,u(1)=ηu(ξ), where 1<α<2, 0<ξ<1, ηξα−1=1, Dα0+ is the standard Riemann-Liouville derivative, f:[0,1]×[0,+∞)→R is continuous. The existence and uniqueness of positive solutions...
| Main Authors: | , |
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| Format: | Journal Article |
| Published: |
SpringerOpen
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/50991 |
| _version_ | 1848758586546585600 |
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| author | Wang, Y. Liu, Lishan |
| author_facet | Wang, Y. Liu, Lishan |
| author_sort | Wang, Y. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we study the nonlocal fractional differential equation:
{Dα0+u(t)+f(t,u(t))=0,0<t<1,u(0)=0,u(1)=ηu(ξ),
where 1<α<2, 0<ξ<1, ηξα−1=1, Dα0+ is the standard Riemann-Liouville derivative, f:[0,1]×[0,+∞)→R is continuous. The existence and uniqueness of positive solutions are obtained by means of the fixed point index theory and iterative technique. |
| first_indexed | 2025-11-14T09:46:21Z |
| format | Journal Article |
| id | curtin-20.500.11937-50991 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:46:21Z |
| publishDate | 2017 |
| publisher | SpringerOpen |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-509912017-09-28T07:28:04Z Positive solutions for a class of fractional 3-point boundary value problems at resonance Wang, Y. Liu, Lishan In this paper, we study the nonlocal fractional differential equation: {Dα0+u(t)+f(t,u(t))=0,0<t<1,u(0)=0,u(1)=ηu(ξ), where 1<α<2, 0<ξ<1, ηξα−1=1, Dα0+ is the standard Riemann-Liouville derivative, f:[0,1]×[0,+∞)→R is continuous. The existence and uniqueness of positive solutions are obtained by means of the fixed point index theory and iterative technique. 2017 Journal Article http://hdl.handle.net/20.500.11937/50991 10.1186/s13662-016-1062-5 http://creativecommons.org/licenses/by/4.0/ SpringerOpen fulltext |
| spellingShingle | Wang, Y. Liu, Lishan Positive solutions for a class of fractional 3-point boundary value problems at resonance |
| title | Positive solutions for a class of fractional 3-point boundary value problems at resonance |
| title_full | Positive solutions for a class of fractional 3-point boundary value problems at resonance |
| title_fullStr | Positive solutions for a class of fractional 3-point boundary value problems at resonance |
| title_full_unstemmed | Positive solutions for a class of fractional 3-point boundary value problems at resonance |
| title_short | Positive solutions for a class of fractional 3-point boundary value problems at resonance |
| title_sort | positive solutions for a class of fractional 3-point boundary value problems at resonance |
| url | http://hdl.handle.net/20.500.11937/50991 |