Heisenberg群上一类半线性方程全局解的存在性

数学季刊 ›› 2004, Vol. 19 ›› Issue (4): 426-435.

Heisenberg群上一类半线性方程全局解的存在性

1. College of Mathematics and Information Science, Henan University, Kaifeng 475001, China; 2.Institute of Mathematics, Henan University, Kaifeng 475001, China; 3. Information Network Center, Henan University, Kaifeng 475001, China; 4. Institute of Applied Mathematics, Northwestern Ploytechnical University, Xi'an 710072, China

收稿日期:2003-11-27 出版日期:2004-12-30 发布日期:2024-03-07
作者简介:ZHENG Zhu-jun(1966-),male,native of Changge,Henan,a profesor of Henan University. Ph.D.,engages in partial diferential equation,mathematics physics.
基金资助:
This work is completed during the frst author visiting the Institute of Theoretical Physics,Chinese Academia of Sciences;the first author is partially supported by the National Science Foundation of P.R.China and outstanding for Youth Foundation of Henan Province and the National Science Foundation of Henan Province,P.R.China.

The Existence of Global Solution for a Class of Semilinear Equations on Heisenberg Group

1. College of Mathematics and Information Science, Henan University, Kaifeng 475001, China; 2.Institute of Mathematics, Henan University, Kaifeng 475001, China; 3. Information Network Center, Henan University, Kaifeng 475001, China; 4. Institute of Applied Mathematics, Northwestern Ploytechnical University, Xi'an 710072, China

Received:2003-11-27 Online:2004-12-30 Published:2024-03-07
About author:ZHENG Zhu-jun(1966-),male,native of Changge,Henan,a profesor of Henan University. Ph.D.,engages in partial diferential equation,mathematics physics.
Supported by:
This work is completed during the first author visiting the Institute of Theoretical Physics,Chinese Academia of Sciences;the first author is partially supported by the National Science Foundation of P.R.China and outstanding for Youth Foundation of Henan Province and the National Science Foundation of Henan Province,P.R.China.

摘要/Abstract

摘要： Based on the concepts of a generalized critical point and the corresponding generalized P.S. condition introduced by Duong Minh Duc [1], we have proved a new Z2 index theorem and get a result on multiplicity of generalized critical points. Using the result and a quite standard variational method, it is found that the equation-ΔH^nu= |u|^p-1u,x∈H has infinite positive solutions. Our approach can also be applied to study more general nonlinear problems.

关键词: subelliptic , operator;Zz index;Heisenberg group;generalized critical point

Abstract: Based on the concepts of a generalized critical point and the corresponding generalized P.S. condition introduced by Duong Minh Duc [1], we have proved a new Z2 index theorem and get a result on multiplicity of generalized critical points. Using the result and a quite standard variational method, it is found that the equation-ΔH^nu= |u|^p-1u,x∈H has infinite positive solutions. Our approach can also be applied to study more general nonlinear problems.

Key words: subelliptic , operator;Zz index;Heisenberg group;generalized critical point

中图分类号:

O175.25

郑驻军, 汪国安, 卢克平, 罗学波. Heisenberg群上一类半线性方程全局解的存在性[J]. 数学季刊, 2004, 19(4): 426-435.

ZHENG Zhu-jun, WANG Guo-an, LU Ke-ping, LUO Xue-bo. The Existence of Global Solution for a Class of Semilinear Equations on Heisenberg Group[J]. Chinese Quarterly Journal of Mathematics, 2004, 19(4): 426-435.

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