Vol. 294, No. 1, 2018

 Recent Issues Vol. 306: 1 Vol. 305: 1  2 Vol. 304: 1  2 Vol. 303: 1  2 Vol. 302: 1  2 Vol. 301: 1  2 Vol. 300: 1  2 Vol. 299: 1  2 Online Archive Volume: Issue:
 The Journal Editorial Board Subscriptions Officers Special Issues Submission Guidelines Submission Form Contacts ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Author Index To Appear Other MSP Journals
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
Milestones
Received: 28 December 2016
Revised: 1 June 2017
Accepted: 11 September 2017
Published: 5 January 2018
Authors
 Jing Li College of Physics and Materials Science College of Mathematics and Information Science Henan Normal University Xinxiang China