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Homoclinic Orbits for a Class of Fractional Hamiltonian Systems via Variational Methods

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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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Acknowledgments

Project supported by National Natural Science Foundation of P. R. China (11271309).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Razi University, Kermanshah, 67149, Iran

    Nemat Nyamoradi

  2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, People’s Republic of China

    Yong Zhou

  3. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Yong Zhou

Authors
  1. Nemat Nyamoradi
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  2. Yong Zhou
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Correspondence to Yong Zhou.

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Nyamoradi, N., Zhou, Y. Homoclinic Orbits for a Class of Fractional Hamiltonian Systems via Variational Methods. J Optim Theory Appl 174, 210–222 (2017). https://doi.org/10.1007/s10957-016-0864-7

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  • DOI: https://doi.org/10.1007/s10957-016-0864-7

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