数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (3): 935-949.doi: 10.1016/S0252-9602(18)30794-X

• 论文 • 上一篇    下一篇

POSITIVE SOLUTIONS FOR A WEIGHTED FRACTIONAL SYSTEM

王朋燕, 王永忠   

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China
  • 收稿日期:2017-05-22 出版日期:2018-06-25 发布日期:2018-06-25
  • 通讯作者: Yongzhong WANG E-mail:wangyz@nwpu.edu.cn
  • 作者简介:Pengyan WANG,E-mail:wangpy119@126.com
  • 基金资助:

    Supported by National Natural Science Foundation of China (11771354).

POSITIVE SOLUTIONS FOR A WEIGHTED FRACTIONAL SYSTEM

Pengyan WANG, Yongzhong WANG   

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China
  • Received:2017-05-22 Online:2018-06-25 Published:2018-06-25
  • Contact: Yongzhong WANG E-mail:wangyz@nwpu.edu.cn
  • Supported by:

    Supported by National Natural Science Foundation of China (11771354).

摘要:

In this article, we study positive solutions to the system

To reach our aim, by using the method of moving planes, we prove a narrow region principle and a decay at infinity by the iteration method. On the basis of these results, we conclude radial symmetry and monotonicity of positive solutions for the problems involving the weighted fractional system on an unit ball and the whole space. Furthermore, non-existence of nonnegative solutions on a half space is given.

关键词: Weighted fractional system, positive solution, radial symmetry, monotonicity, non-existence

Abstract:

In this article, we study positive solutions to the system

To reach our aim, by using the method of moving planes, we prove a narrow region principle and a decay at infinity by the iteration method. On the basis of these results, we conclude radial symmetry and monotonicity of positive solutions for the problems involving the weighted fractional system on an unit ball and the whole space. Furthermore, non-existence of nonnegative solutions on a half space is given.

Key words: Weighted fractional system, positive solution, radial symmetry, monotonicity, non-existence