Symmetry of standing waves for two kinds of fractional Hardy-Schrödinger equations

Abstract In this paper, we consider two kinds of nonlinear Schrodinger equations with the fractional Laplacian and Hardy potential ( λ | x | s , 0 λ ⩽ λ ∗ , λ ∗ is a constant of the Hardy-Sobolev inequality), which represent the generalized form of Hartree and Pekar-Choquard type time dependent fractional Hardy-Schrodinger equations. Applying the direct method of moving planes, we obtain the radial symmetry and monotonicity of the standing waves for the given equations.