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The Applications of Critical-Point Theory to Discontinuous Fractional-Order Differential Equations

Published online by Cambridge University Press:  16 March 2017

Yu Tian*
Affiliation:
School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, People's Republic of China (tianyu2992@163.com)
Juan J. Nieto
Affiliation:
Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain Faculty of Science, King Abdulaziz University, PO Box 80203, 21589, Jeddah, Saudi Arabia
*
*Corresponding author.

Abstract

We consider a fractional equation involving the left and right Riemann–Liouville fractional integrals and with Sturm–Liouville boundary-value conditions. We establish the variational structure of the problem and, by using critical-point theory, the existence of an unbounded sequence of solutions is obtained.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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