Weak solutions to boundary value problems for fractional differential equations via variational methods
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Authors
Peiluan Li
- School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, P. R. China.
Changjin Xu
- Guizhou Key Laboratory of Economics System Simulation, Guizhou College of Finance and Economics, Guiyang, 550004, P. R. China.
Hui Wang
- College of Information Engineering, Henan University of Science and Technology, Luoyang, 471003, P. R. China.
Abstract
Using variational methods, we investigate the solutions to the boundary value problems for fractional
order differential equations. First, we consider the eigenvalue problem associated with it. Then, we obtain
the existence of at least two weak solutions for every real number via Brezis and Nirenberg's Linking
Theorem. Furthermore, for every positive integer k, the existence criteria of k pairs of weak solutions are
established by using Clark Theorem. At last, some examples are also given to illustrate the results.
Share and Cite
ISRP Style
Peiluan Li, Changjin Xu, Hui Wang, Weak solutions to boundary value problems for fractional differential equations via variational methods, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 2971--2981
AMA Style
Li Peiluan, Xu Changjin, Wang Hui, Weak solutions to boundary value problems for fractional differential equations via variational methods. J. Nonlinear Sci. Appl. (2016); 9(5):2971--2981
Chicago/Turabian Style
Li, Peiluan, Xu, Changjin, Wang, Hui. "Weak solutions to boundary value problems for fractional differential equations via variational methods." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 2971--2981
Keywords
- Fractional differential equations
- critical points
- variational method
- eigenvalue problem.
MSC
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