Homoclinic solutions for fractional discrete Laplacian equations. (September 2020)

• Record Type: Journal Article
• Authors: Xiang, Mingqi; Zhang, Binlin
• Is Part Of: Nonlinear analysis. Volume 198(2020)
• Publication Date: 2020-09
• Subjects: 35R11 -- 49M25 -- 35K05; Fractional discrete Laplacian -- Homoclinic solutions -- Variational methods -- Multiplicity of solutions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111886
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we introduce a variational framework to a fractional difference equation on Z driven by the fractional discrete Laplacian and involving a coercive weight function and a positive parameter λ . By means of the critical point theory, we prove the existence of at least two nontrivial and nonnegative homoclinic solutions for λ big enough.