Existence of solutions to fractional differential equations with multi-point boundary conditions at resonance in Hilbert spaces
This article is devoted to investigating the existence of solutions to fractional multi-point boundary-value problems at resonance in a Hilbert space. More precisely, the dimension of the kernel of the fractional differential operator with the boundary conditions be any positive integer. We po...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Texas State University
2016-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/61/abstr.html |
| _version_ | 1819240523888590848 |
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| author | Hua-Cheng Zhou Fu-Dong Ge Chun-Hai Kou |
| author_facet | Hua-Cheng Zhou Fu-Dong Ge Chun-Hai Kou |
| author_sort | Hua-Cheng Zhou |
| collection | DOAJ |
| description | This article is devoted to investigating the existence of solutions
to fractional multi-point boundary-value problems at resonance
in a Hilbert space. More precisely, the dimension of the kernel
of the fractional differential operator with the boundary conditions
be any positive integer. We point out that the problem is new even
when the system under consideration is reduced to a second-order
ordinary differential system with resonant boundary conditions.
We show that the considered system admits at least a solution by applying
coincidence degree theory first introduced by Mawhin.
An example is presented to illustrate our results. |
| first_indexed | 2024-12-23T14:09:22Z |
| format | Article |
| id | doaj.art-e58e49f31f754a56acaccb73294466a6 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-23T14:09:22Z |
| publishDate | 2016-02-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-e58e49f31f754a56acaccb73294466a62022-12-21T17:44:05ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912016-02-01201661,116Existence of solutions to fractional differential equations with multi-point boundary conditions at resonance in Hilbert spacesHua-Cheng Zhou0Fu-Dong Ge1Chun-Hai Kou2 Academia Sinica, Beijing, China Donghua Univ., Shanghai 201620, China Donghua Univ., Shanghai 201620, China This article is devoted to investigating the existence of solutions to fractional multi-point boundary-value problems at resonance in a Hilbert space. More precisely, the dimension of the kernel of the fractional differential operator with the boundary conditions be any positive integer. We point out that the problem is new even when the system under consideration is reduced to a second-order ordinary differential system with resonant boundary conditions. We show that the considered system admits at least a solution by applying coincidence degree theory first introduced by Mawhin. An example is presented to illustrate our results.http://ejde.math.txstate.edu/Volumes/2016/61/abstr.htmlFractional differential equationsresonancecoincidence degree |
| spellingShingle | Hua-Cheng Zhou Fu-Dong Ge Chun-Hai Kou Existence of solutions to fractional differential equations with multi-point boundary conditions at resonance in Hilbert spaces Electronic Journal of Differential Equations Fractional differential equations resonance coincidence degree |
| title | Existence of solutions to fractional differential equations with multi-point boundary conditions at resonance in Hilbert spaces |
| title_full | Existence of solutions to fractional differential equations with multi-point boundary conditions at resonance in Hilbert spaces |
| title_fullStr | Existence of solutions to fractional differential equations with multi-point boundary conditions at resonance in Hilbert spaces |
| title_full_unstemmed | Existence of solutions to fractional differential equations with multi-point boundary conditions at resonance in Hilbert spaces |
| title_short | Existence of solutions to fractional differential equations with multi-point boundary conditions at resonance in Hilbert spaces |
| title_sort | existence of solutions to fractional differential equations with multi point boundary conditions at resonance in hilbert spaces |
| topic | Fractional differential equations resonance coincidence degree |
| url | http://ejde.math.txstate.edu/Volumes/2016/61/abstr.html |
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