环绕定理在退化的椭圆型方程上的应用

数学物理学报 ›› 2023, Vol. 43 ›› Issue (6): 1759-1773.

环绕定理在退化的椭圆型方程上的应用

周英告(),李周欣^*()

中南大学数学与统计学院长沙 410083

收稿日期:2023-01-05 修回日期:2023-04-12 出版日期:2023-12-26 发布日期:2023-11-16
通讯作者: *李周欣，E-mail: lzx@math.pku.edu.cn
作者简介:周英告，E-mail: ygzhou@csu.edu.cn
基金资助:
湖南省研究生教育教学改革研究项目(2020JGYB031);中南大学教育教学改革研究项目(2020JGB020);中南大学教育教学改革研究项目(2022ALK006);中南大学教育教学改革研究项目(2022jy069);湖南省自然科学基金(2023JJ30645)

An Application of Linking Theorem to Degenerative Elliptic Equations

Zhou Yinggao(),Li Zhouxin^*()

School of Mathematical and Statistics, Central South University, Changsha 410083

Received:2023-01-05 Revised:2023-04-12 Online:2023-12-26 Published:2023-11-16
Supported by:
Degree and Graduate Education Reform Research Project of Hunan Province(2020JGYB031);Education and Teaching Reform Research Project of Central South University(2020JGB020);Education and Teaching Reform Research Project of Central South University(2022ALK006);Education and Teaching Reform Research Project of Central South University(2022jy069);Hunan Provincial Natural Science Foundation(2023JJ30645)

摘要/Abstract

摘要：

该文考虑一类带临界增长项的退化的椭圆型偏微分方程解的存在性, 利用变量代换的方法, 把方程转化为半线性方程, 再利用集中紧引理以及基于锥分解的环绕定理, 证明了方程解的存在性.

关键词: 椭圆型方程, 环绕定理, 临界指数

Abstract:

In this paper, we study a class of degenerative quasilinear elliptic equations with critical exponent. Using a change of variable, we reformulate the equation into a semilinear one, and prove the existence of solutions by employing Lions concentration compactness principle and linking theorem based on cone.

Key words: Elliptic equations, Linking thoerem, Critical exponent

中图分类号:

O177.91

周英告, 李周欣. 环绕定理在退化的椭圆型方程上的应用[J]. 数学物理学报, 2023, 43(6): 1759-1773.

Zhou Yinggao, Li Zhouxin. An Application of Linking Theorem to Degenerative Elliptic Equations[J]. Acta mathematica scientia,Series A, 2023, 43(6): 1759-1773.

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