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

Abstract

In this paper, we consider two kinds of nonlinear Schrödinger 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-Schrödinger equations. Applying the direct method of moving planes, we obtain the radial symmetry and monotonicity of the standing waves for the given equations.

Keywords

• 35R11
• 35J60
• 35J10