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Multiplicity of Homoclinic solutions for fractional discrete $p-$Laplacian equations
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  • Jiabin Zuo,
  • Tahar Bouali,
  • Rafik GUEFAIFIA,
  • Libo Yang
Jiabin Zuo
Guangzhou University
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Tahar Bouali
University of Larbi Tebessi-Informatics and systemes
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Larbie tebessi University, Tebessa, Algeria.
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Libo Yang
Huaiyin Institute of Technology

Corresponding Author:[email protected]

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In this study, we investigate the existence and multiplicity of solutions for a fractional discrete $p-$ Laplacian equation on $ \mathbb{Z} $, via the mountain pass lemma and Ekeland’s variational principle. Under suitable hypotheses on functions $V$ and $f$, we prove that this equation admits at least two nonnegative and nontrivial homoclinic solutions when the real parameter $\lambda >0$ is large enough.