Electron. J. Diff. Equ., Vol. 2016 (2016), No. 61, pp. 1-16.

Existence of solutions to fractional differential equations with multi-point boundary conditions at resonance in Hilbert spaces

Hua-Cheng Zhou, Fu-Dong Ge, Chun-Hai Kou

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.

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Hua-Cheng Zhou
Academy of Mathematics and Systems Science
Academia Sinica
Beijing 100190, China
email: hczhou@amss.ac.cn
Fu-Dong Ge
College of Information Science and Technology
Donghua University
Shanghai 201620, China
email: gefd2011@gmail.com
Chun-Hai Kou
Department of Applied Mathematics
Donghua University
Shanghai 201620, China
email: kouchunhai@dhu.edu.cn

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