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The Existence and Multiplicity of Homoclinic Solutions for a Fractional Discrete p −Laplacian Equation

Author

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  • Yong Wu

    (School of Tourism Data, Guilin Tourism University, Guilin 541006, China)

  • Bouali Tahar

    (Department of Mathematics, College of Sciences, Jazan University, Jazan 45142, Saudi Arabia
    Department of Mathematics and Computer Science, Larbi Tebessi University, Tebessa 12002, Algeria)

  • Guefaifia Rafik

    (Laboratory of Mathematics, Informatics and Systemes (LAMIS), Larbi Tebessi University, Tebessa 12000, Algeria)

  • Abita Rahmoune

    (Laboratory of Pure and Applied Mathematics, University of Laghouat, P.O. Box 37G, Laghouat 03000, Algeria)

  • Libo Yang

    (Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huai’an 223003, China)

Abstract

In this study, we investigate the existence and multiplicity of solutions for a fractional discrete p −Laplacian equation on Z . Under suitable hypotheses on the potential function V and the nonlinearity f , with the aid of Ekeland’s variational principle, via mountain pass lemma, we obtain that this equation exists at least two nonnegative and nontrivial homoclinic solutions when the real parameter λ > 0 is large enough.

Suggested Citation

  • Yong Wu & Bouali Tahar & Guefaifia Rafik & Abita Rahmoune & Libo Yang, 2022. "The Existence and Multiplicity of Homoclinic Solutions for a Fractional Discrete p −Laplacian Equation," Mathematics, MDPI, vol. 10(9), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1400-:d:799600
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    References listed on IDEAS

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    1. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    2. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
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    Cited by:

    1. Ju, Chunming & Zhang, Binlin, 2022. "On fractional discrete p-Laplacian equations via Clark’s theorem," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    2. Limin Chu & Weimin Hu & Youhui Su & Yongzhen Yun, 2022. "Existence and Uniqueness of Solutions to Four-Point Impulsive Fractional Differential Equations with p -Laplacian Operator," Mathematics, MDPI, vol. 10(11), pages 1-30, May.

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