Abstract
In this paper, by applying the direct method of moving planes, the authors study the radial symmetry of standing waves for nonlinear fractional Laplacian Schrödinger systems with Hardy potential. Firstly, under the condition of infinite decay, the radial symmetry of the solution is established. Secondly, under the condition of no decay, the radial symmetry and non-existence of solution are established by the Kelvin transform.
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