Hua-Cheng Zhou, Fu-Dong Ge, Chun-Hai Kou
Abstract:
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.
Submitted August 22, 2015. Published February 29, 2016.
Math Subject Classifications: 34A08, 34B10, 34B40.
Key Words: Fractional differential equations; resonance; coincidence degree.
Show me the PDF file (274 KB), TEX file for this article.
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Hua-Cheng Zhou Academy of Mathematics and Systems Science Academia Sinica Beijing 100190, China email: hczhou@amss.ac.cn |
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Fu-Dong Ge College of Information Science and Technology Donghua University Shanghai 201620, China email: gefd2011@gmail.com |
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Chun-Hai Kou Department of Applied Mathematics Donghua University Shanghai 201620, China email: kouchunhai@dhu.edu.cn |
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