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Variational Approach to Homoclinic Solutions for Fractional Hamiltonian Systems

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Abstract

In this paper, we discuss the existence and multiplicity of homoclinic solutions for fractional Hamiltonian systems with left and right Liouville–Weyl fractional derivatives. Sufficient conditions ensuring the existence of an unbounded sequence of homoclinic solutions for the given problem are obtained via variational approach.

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Acknowledgements

Yong Zhou acknowledges the support by National Natural Science Foundation of China (11671339). The authors thank the editor for his useful comments that led to the improvement of the original manuscript.

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Authors and Affiliations

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

    Nemat Nyamoradi

  2. Faculty of Mathematics and Computational Science, Xiangtan University, Hunan, 411105, China

    Yong Zhou

  3. Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Yong Zhou, Bashir Ahmad & Ahmed Alsaedi

Authors
  1. Nemat Nyamoradi
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  2. Yong Zhou
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  3. Bashir Ahmad
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  4. Ahmed Alsaedi
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Correspondence to Yong Zhou or Bashir Ahmad.

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Nyamoradi, N., Zhou, Y., Ahmad, B. et al. Variational Approach to Homoclinic Solutions for Fractional Hamiltonian Systems. J Optim Theory Appl 174, 223–237 (2017). https://doi.org/10.1007/s10957-017-1086-3

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  • DOI: https://doi.org/10.1007/s10957-017-1086-3

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