Vol. 290, No. 2, 2017

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 292: 1
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Vol. 286: 1  2
Vol. 285: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
A direct method of moving planes for the system of the fractional Laplacian

Chunxia Cheng, Zhongxue Lü and Yingshu Lü

Vol. 290 (2017), No. 2, 301–320
Abstract

We establish a direct method of moving planes for systems of fractional Laplacian equations. By using this direct method of moving planes, we obtain symmetry and nonexistence of positive solutions for the following system of fractional Laplacian equations:

(Δ)α2u(x) = vq(x),x n, (Δ)α2v(x) = up(x),x n.
Keywords
the fractional Laplacian, maximum principles for antisymmetric functions, narrow region principle, decay at infinity, method of moving planes, radial symmetry, nonexistence of positive solutions
Mathematical Subject Classification 2010
Primary: 35B09, 35B50, 35B53, 35J61
Milestones
Received: 29 November 2015
Revised: 13 October 2016
Accepted: 14 December 2016
Published: 25 July 2017
Authors
Chunxia Cheng
School of Mathematics and Statistics
Jiangsu Normal University
Xuzhou, 221116
China
Zhongxue Lü
School of Mathematics and Statistics
Jiangsu Normal University
Xuzhou, 221116
China
Yingshu Lü
Department of Mathematics
Shanghai Jiao Tong University
Shanghai, 200240
China