Symmetry of components and Liouville-type theorems for semilinear elliptic systems involving the fractional Laplacian. (March 2019)

• Record Type: Journal Article
• Authors: Yang, Hui; Zou, Wenming
• Is Part Of: Nonlinear analysis. Volume 180(2019)
• Page Start: 208
• Page End: 224
• Publication Date: 2019-03
• Subjects: 35B06 -- 35B53 -- 35J65 -- 35R11; Nonlinear elliptic systems -- Fractional Laplacian -- Symmetry -- Liouville type theorems; 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.2018.10.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study the symmetry of components of positive solutions for the fractional elliptic systems in the whole space R N . As an application, we prove the uniqueness of positive solutions for fractional Schrödinger type systems with critical exponents. We also prove the symmetry of components and some Liouville type theorems for a class of fractional noncooperative systems, which contains the systems arising in Bose–Einstein condensation and in biological models of Lotka–Volterra type.