Monotonicity of positive solutions for fractional p-systems in unbounded Lipschitz domains. (September 2020)

• Record Type: Journal Article
• Authors: Ma, Lingwei; Zhang, Zhenqiu
• Is Part Of: Nonlinear analysis. Volume 198(2020)
• Publication Date: 2020-09
• Subjects: 35R11 -- 35B50 -- 35B99; Fractional p-Laplacian -- Cooperative systems -- Narrow region principle in unbounded domains -- Direct method of moving planes -- Sliding method -- Monotonicity 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.2020.111892
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, without imposing any decay assumptions on the solutions at infinity, we first develop an unbounded narrow region principle for the fractional p -Laplacian systems, an essential ingredient to carry on the direct method of moving planes; then we combine this direct method with the sliding method to obtain the monotonicity of positive bounded solutions for cooperative systems involving the fractional p -Laplacian in unbounded Lipschitz domains. We believe that the new ideas introduced here will become useful tools in studying qualitative properties of solutions for other types of nonlinear nonlocal systems in various unbounded domains.