Symmetry of positive solutions of fractional Laplacian equation and system with Hardy–Sobolev exponent on the unit ball

Abstract

In this work, we consider a class of Hardy–Sobolev differential equations and systems involving the fractional Laplacian on the unit ball. We first show the differential equations and systems are equivalent to some integral equations and systems, respectively. Then applying the method of moving planes in the integral forms, we prove the radial symmetry of positive solutions.