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

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

作　　者：张书陶[1] 韩亚洲[1] Zhang Shutao Han Yazhou(Department of Mathematics, College of Science, China Jiliang University, Hangzhou 310018)

机构地区：[1]中国计量大学理学院数学系

出　　处：《数学物理学报（A辑）》2017年第2期278-286,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(11201443);浙江省自然科学基金(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.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.

关 键 词：移动球面法 HEISENBERG群 LIOUVILLE型定理 半线性方程 

分 类 号：O175.2[理学—数学]