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Multiplicity Solutions for a Class of Fractional Hamiltonian Systems With Concave–Convex Potentials

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Abstract

In this paper, we study the existence and nonuniqueness of nontrivial solutions for a class of fractional Hamiltonian systems with concave–convex potentials via the variational methods. A new twisted condition is introduced, which yields a new compact embedding theorem. Some results are new even for second-order Hamiltonian systems.

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Authors and Affiliations

  1. College of Science, Southwest Petroleum University, Chengdu, 610500, Sichuan, People’s Republic of China

    Dong-Lun Wu

  2. Institute of Nonlinear Dynamics, Southwest Petroleum University, Chengdu, 610500, Sichuan, People’s Republic of China

    Dong-Lun Wu

  3. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Chun Li & Pengfei Yuan

Authors
  1. Dong-Lun Wu
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  2. Chun Li
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  3. Pengfei Yuan
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Corresponding author

Correspondence to Dong-Lun Wu.

Additional information

This work was supported by National Natural Science Foundation of China (no. 11626198), the Young scholars development fund of Southwest Petroleum University (SWPU) (Grant no. 201599010116) and the Fundamental Research Funds for the Central Universities (no. XDJK2014B041).

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Wu, DL., Li, C. & Yuan, P. Multiplicity Solutions for a Class of Fractional Hamiltonian Systems With Concave–Convex Potentials. Mediterr. J. Math. 15, 35 (2018). https://doi.org/10.1007/s00009-018-1079-y

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  • DOI: https://doi.org/10.1007/s00009-018-1079-y

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