Radial symmetry of positive solutions of an integral system associated with the reversed Stein-Weiss inequality

Abstract

Whether the solutions of conformal equations in the whole space are radially symmetric is an interesting topic. Chen-Li-Ou proved the radial symmetry for integral systems of the Hardy-Littlewood-Sobolev type and the Stein-Weiss type by the method of moving planes in integral form. In 2015, Dou-Zhu obtained the radial symmetry of extremal functions of the reversed Hardy-Littlewood-Sobolev inequality by the method of moving spheres, and Liu proved the radial symmetry of solutions of the Euler-Lagrange system by the method of moving planes developed by Dou-Guo-Zhu. In this paper, we also use the method of moving planes to prove the radial symmetry of positive solutions of the Euler-Lagrange system satisfied by the extremal functions of the reversed Stein-Weiss inequality established by Chen-Liu-Lu-Tao in 2018.