数学物理学报 ›› 2017, Vol. 37 ›› Issue (2): 278-286.

• 论文 • 上一篇    下一篇

Heisenberg群上移动球面法的应用——一类半线性方程的Liouville型定理

张书陶, 韩亚洲   

  1. 中国计量大学理学院数学系 杭州 310018
  • 收稿日期:2016-07-26 修回日期:2017-01-15 出版日期:2017-04-26 发布日期:2017-04-26
  • 通讯作者: 韩亚洲 E-mail:yazhou.han@gmail.com
  • 作者简介:张书陶,taoer558@163.com
  • 基金资助:
    国家自然科学基金(11201443)和浙江省自然科学基金(LY16A010009)

An Application of the Method of Moving Sphere in the Heisenberg Group——Liouville Type Theorem of a Class of Semilinear Equations

Zhang Shutao, Han Yazhou   

  1. Department of Mathematics, College of Science, China Jiliang University, Hangzhou 310018
  • Received:2016-07-26 Revised:2017-01-15 Online:2017-04-26 Published:2017-04-26
  • Supported by:
    Supported by the NSFC (11201443) and the Natural Science Foundation of Zhejiang Province (LY16A010009)

摘要: 作为Heisenberg群上移动球面法的基础,在Heisenberg群上引入了一类CR反演变换.作为应用,讨论了Heisenberg群上的次临界方程,证明任意非负柱对称解均为平凡解.

关键词: 移动球面法, Heisenberg群, Liouville型定理, 半线性方程

Abstract: Firstly, a class of CR inversion in the Heisenberg group was introduced. This is the foundation of the method of moving sphere. As an application, we discussed a class of subcritical equations in the Heisenberg group and obtained the nonexistence of positive solutions with cylindrical symmetry.

Key words: Method of moving sphere, Heisenberg group, Liouville type theorem, Semilinear equation

中图分类号: 

  • O175.2