Radial symmetry results for fractional Laplacian systems. (November 2016)

• Record Type: Journal Article
• Authors: Liu, Baiyu; Ma, Li
• Is Part Of: Nonlinear analysis. Volume 146(2016)
• Page Start: 120
• Page End: 135
• Publication Date: 2016-11
• Subjects: 35R11 -- 35A01; Fractional Laplacian system -- Method of moving planes -- Radial symmetry; 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.2016.08.022
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we generalize the direct method of moving planes for the fractional Laplacian to the system case. Considering a coupled nonlinear system with fractional Laplacian, we first establish a decay at infinity principle and a narrow region principle. Using these principles, we then obtain two radial symmetry results for the decaying solutions of the fractional Laplacian systems. Finally, we apply our method to fractional Schrödinger systems and fractional Hénon systems.