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

Part of: General theory in ordinary differential equations Variational problems in infinite-dimensional spaces

Published online by Cambridge University Press:  16 March 2017

Yu Tian  and
Juan J. Nieto
Yu Tian*
Affiliation:
School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, People's Republic of China ([email protected])
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.
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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.

Keywords

fractional differential equationdiscontinuousSturm–Liouville boundary conditionscritical-point theory

MSC classification

Secondary: 34A36: Discontinuous equations 34A08: Fractional differential equations 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel'man) theory, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 4 , November 2017 , pp. 1021 - 1051
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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