Radial symmetry of standing waves for nonlinear fractional Hardy-Schrödinger equation

Abstract In this paper, by applying the method of moving planes, we conclude the conclusions for the radial symmetry of standing waves for a nonlinear Schrodinger equation involving the fractional Laplacian and Hardy potential. First, we prove the radial symmetry of solution under the condition of decay near infinity. Based upon that, under the condition of no decay, by the Kelvin transform, we establish the results for the non-existence and radial symmetry of solution.