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Journal of Function Spaces
Volume 2016, Article ID 2941368, 9 pages
http://dx.doi.org/10.1155/2016/2941368
Research Article

Solutions for Impulsive Fractional Differential Equations via Variational Methods

1School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
2College of Information Engineering, Henan University of Science and Technology, Luoyang 471023, China
3Network and Information Center, Henan University of Science and Technology, Luoyang 471023, China

Received 20 January 2016; Accepted 16 March 2016

Academic Editor: Jozef Banas

Copyright © 2016 Peiluan Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the boundary value problems of impulsive fractional order differential equations. First, we obtain the existence of at least one solution by the minimization result of Mawhin and Willem. Then by the variational methods and a very recent critical points theorem of Bonanno and Marano, the existence results of at least triple solutions are established. At last, two examples are offered to demonstrate the application of our main results.