Heisenberg群上一类含有临界Sobolev指数拟线性椭圆方程存在性定理

数学物理学报 ›› 2017, Vol. 37 ›› Issue (3): 478-490.

Heisenberg群上一类含有临界Sobolev指数拟线性椭圆方程存在性定理

刘莉静, 刘晓春

武汉大学数学与统计学院武汉 430072

收稿日期:2016-09-12 修回日期:2017-01-13 出版日期:2017-06-26 发布日期:2017-06-26
作者简介:刘莉静,E-mail:liulijng523@163.com;刘晓春,E-mail:xcliu@whu.edu.cn
基金资助:
国家自然科学基金（11171261，11371282）

The Existence Theorem for a Qusi-Linear Elliptic Equations Involving Critical Sobolev Exponent on the Heisenberg Group

Liu Lijing, Liu Xiaochun

School of Mathematics and Statistics, Wuhan University, Wuhan 430072

Received:2016-09-12 Revised:2017-01-13 Online:2017-06-26 Published:2017-06-26
Supported by:
Supported by the NSFC (11171261, 11371282)

摘要/Abstract

摘要： 研究了Heisenberg群上一类含有临界Sobolev指数的偏微分方程解的存在性问题.利用Nehari流形以及极值原理，证明了在不同的条件下，方程至少存在一个或两个正解.

关键词: Heisenberg群, Nehari流形, 临界Sobolev指数

Abstract: In this paper, we study the partial differential equations on the Heisenberg group with a singular potential and critical Sobolev exponent. With the help of Nehari manifold, we prove that our problem has at least one or two positive solutions under different conditions. The result generalized the corresponding result in Euclidean space.

Key words: Heisenberg group, Nehari manifoid, Critical Sobolev exponent

中图分类号:

O175.2

刘莉静, 刘晓春. Heisenberg群上一类含有临界Sobolev指数拟线性椭圆方程存在性定理[J]. 数学物理学报, 2017, 37(3): 478-490.

Liu Lijing, Liu Xiaochun. The Existence Theorem for a Qusi-Linear Elliptic Equations Involving Critical Sobolev Exponent on the Heisenberg Group[J]. Acta mathematica scientia,Series A, 2017, 37(3): 478-490.

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