Asymptotic and optimal Liouville properties for Wolff type integral systems. (January 2016)

• Record Type: Journal Article
• Authors: Villavert, John
• Is Part Of: Nonlinear analysis. Volume 130(2015)
• Page Start: 102
• Page End: 120
• Publication Date: 2016-01
• Subjects: primary 45G05 45G15 45M05 -- secondary 35B40 35J62; Liouville theorem -- Quasilinear system -- Wolff potential; 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.2015.09.017
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This article examines the properties of positive solutions to fully nonlinear systems of integral equations involving Hardy and Wolff potentials. The first part of the paper establishes an optimal existence result and a Liouville type theorem for the integral systems. Then, the second part examines the decay rates of positive bound states at infinity. In particular, a complete characterization of the asymptotic properties of bounded and decaying solutions is given by showing that such solutions vanish at infinity with two principle rates: the slow decay rates and the fast decay rates. In fact, the two rates can be fully distinguished by an integrability criterion. As an application, the results are shown to carry over to certain systems of quasilinear equations.