Radial symmetry of solution for fractional p−Laplacian system

Abstract In this paper, we investigate the method of moving planes for fractional p -Laplacian system. We firstly discuss the key ingredients for the method of moving planes such as maximum principle for anti-symmetric functions, decay at infinity and boundary estimate. Then we apply the method of moving planes to establish the radial symmetry and the monotonicity of the positive solutions for fractional p − Laplacian system in a unit ball or in the whole space.