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Entropy 2017, 19(2), 50; doi:10.3390/e19020050

Multiplicity of Homoclinic Solutions for Fractional Hamiltonian Systems with Subquadratic Potential

1
Department of Mathematics, Faculty of Sciences, Razi University, Kermanshah 67149, Iran
2
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3
Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editors: António M. Lopes and J. A. Tenreiro Machado
Received: 24 November 2016 / Revised: 11 January 2017 / Accepted: 19 January 2017 / Published: 24 January 2017
(This article belongs to the Special Issue Complex Systems and Fractional Dynamics)
View Full-Text   |   Download PDF [326 KB, uploaded 25 January 2017]

Abstract

In this paper, we study the existence of homoclinic solutions for the fractional Hamiltonian systems with left and right Liouville–Weyl derivatives. We establish some new results concerning the existence and multiplicity of homoclinic solutions for the given system by using Clark’s theorem from critical point theory and fountain theorem. View Full-Text
Keywords: homoclinic solutions; fractional Hamiltonian systems; critical point theory homoclinic solutions; fractional Hamiltonian systems; critical point theory
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. (CC BY 4.0).

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Nyamoradi, N.; Alsaedi, A.; Ahmad, B.; Zhou, Y. Multiplicity of Homoclinic Solutions for Fractional Hamiltonian Systems with Subquadratic Potential. Entropy 2017, 19, 50.

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