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Infinitely many solutions for fractional differential system via variational method

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Abstract

In this paper we investigate a boundary value problem for a coupled nonlinear differential system of fractional order. Under appropriate hypotheses and by applying the critical point theorem, we obtain some new criteria to guarantee that the fractional differential system has infinitely many weak solutions. In addition, an example is given to illustrate the main results.

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Acknowledgments

The research is supported by Hunan Provincial Natural Science Foundation of China (No. 13JJ3106), and by National Natural Science Foundation of China (Nos. 11271372 and 11201138), and also by Aid program for Science and Technology Innovative Research Team in Higher Educational Instituions of Hunan Province.

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Authors and Affiliations

  1. School of Science, Hunan University of Technology, Zhuzhou, 412007, Hunan, People’s Republic of China

    Yulin Zhao & Qiming Zhang

  2. Department of Mathematics, Central South University, Changsha, 410075, Hunan, People’s Republic of China

    Haibo Chen

Authors
  1. Yulin Zhao
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  2. Haibo Chen
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  3. Qiming Zhang
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Correspondence to Yulin Zhao.

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Zhao, Y., Chen, H. & Zhang, Q. Infinitely many solutions for fractional differential system via variational method. J. Appl. Math. Comput. 50, 589–609 (2016). https://doi.org/10.1007/s12190-015-0886-6

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  • DOI: https://doi.org/10.1007/s12190-015-0886-6

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