#### Vol. 294, No. 1, 2018

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Monotonicity and radial symmetry results for Schrödinger systems with fractional diffusion

### Jing Li

Vol. 294 (2018), No. 1, 107–121
##### Abstract

We consider a nonlinear Schrödinger system with fractional diffusion

where $\Omega$ is an unbounded parabolic domain. We first establish a narrow region principle. Using this principle and a direct method of moving planes, we obtain the monotonicity of nonnegative solutions and the Liouville-type result for the nonlinear Schrödinger system with fractional diffusion. We also obtain the radially symmetric result of positive solutions for the system in the unit ball when $A\left(x\right)$ and $B\left(x\right)$ are constants.

##### Keywords
fractional Schrödinger system, narrow region principle, direct method of moving planes, monotonicity, radially symmetric
Primary: 35J60