Radial symmetry results for fractional Laplacian systems

TL;DR

This paper extends the method of moving planes to fractional Laplacian systems, establishing symmetry results for solutions and applicable to various fractional PDE systems.

Contribution

It introduces a novel approach for proving radial symmetry in fractional Laplacian systems, including decay and narrow region principles.

Findings

Established decay at infinity principle.

Proved radial symmetry for fractional Laplacian systems.

Applicable to fractional Schrödinger and Hénon systems.

Abstract

In this paper, we generalize the direct method of moving planes for the fractional Laplacian to the system case. Considering a coupled nonlinear system with fractional Laplacian, we first establish a decay at infinity principle and a narrow region principle. Using these principles, we obtain two radial symmetry results for the decaying solutions of the fractional Laplacian systems. Our method can be applied to fractional Schr\"odinger systems and fractional H\'enon systems.