Symmetry and Uniqueness of Solutions of an Integral System

Abstract

In this paper, we study the positive solutions for a class of integral systems and prove that all the solutions are radially symmetric and monotonically decreasing about some point. Moreover, we also obtain the uniqueness result for a special case. We use a new type of moving plane method introduced by Chen-Li-Ou [1]. Our new ingredient is the use of Hardy-Littlewood-Sobolev inequality instead of Maximum Principle.