Homoclinic Orbits for a Class of Fractional Hamiltonian Systems via Variational Methods |
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| Authors: | Nemat Nyamoradi Yong Zhou |
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| Institution: | 1.Department of Mathematics, Faculty of Sciences,Razi University,Kermanshah,Iran;2.School of Mathematics and Computational Science,Xiangtan University,Xiangtan,People’s Republic of China;3.Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science,King Abdulaziz University,Jeddah,Saudi Arabia |
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| Abstract: | This paper is devoted to the existence and multiplicity of homoclinic orbits for a class of fractional-order Hamiltonian systems with left and right Liouville–Weyl fractional derivatives. Here, we present a new approach via variational methods and critical point theory to obtain sufficient conditions under which the Hamiltonian system has at least one homoclinic orbit or multiple homoclinic orbits. Some results are new even for second-order Hamiltonian systems. |
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