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

Yong Wu, Bouali Tahar, Guefaifia Rafik, Abita Rahmoune and Libo Yang
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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
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

Mathematics, 2022, vol. 10, issue 9, 1-16

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.

Keywords: fractional discrete p ?Laplace equation; mountain pass lemma; homoclinic solutions; Ekeland’s variational principle; multiplicity of solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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