| 变分方法及其在非线性偏微分方程应用方面的进展和未决问题 |
| |
| 引用本文： | 邹文明.变分方法及其在非线性偏微分方程应用方面的进展和未决问题[J].江西师范大学学报(自然科学版),2018,0(2):111-129207. |
| |
| 作者姓名： | 邹文明 |
| |
| 作者单位： | 清华大学数学科学系,北京 100084 |
| |
| 摘 要： | 先介绍变分法发展的简单历史以及将来的发展趋势. 然后综述变分法应用于非线性偏微分方程的基本思想和最新成果. 通俗介绍环绕理论、变号临界点理论及应用,其中包括对称扰动方程和Rabinowitz公开问题、Brezis-Nirenberg临界指数方程、Li-Lin公开问题、Bose-Einstein凝聚、Berestycki-Caffarelli-Nirenberg猜测和Lane-Emden方程及猜想.
|
| 关 键 词： | 变分法 非线性偏微分方程 环绕理论 临界指数 变号临界点理论 薛定谔方程 |
Results and Open Problems of the Variational Method with Applications to Nonlinear Partial Differential Equations |
| |
| ZOU Wenming.Results and Open Problems of the Variational Method with Applications to Nonlinear Partial Differential Equations[J].Journal of Jiangxi Normal University (Natural Sciences Edition),2018,0(2):111-129207. |
| |
| Authors: | ZOU Wenming |
| |
| Institution: | Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China |
| |
| Abstract: | The brief history and the development trend of the variational method are introduced.Then the fundamental ideas and the latest achievements of the variational method with applications to nonlinear partial differential equations are summarized.The critical point theory and its applications are briefly reviewed,including the perturbed equation from symmetry,Rabinowitz's open problem,Brezis-Nirenberg's critical exponent equation,Li-Lin's open problem,Bose-Einstein condensation,Berestycki-Caffarelli-Nirenberg's conjecture and Lane-Emden's equation and conjecture. |
| |
| Keywords: | variational method nonlinear partial differential equations linking theory critical exponent critical point theory Schrödinger equations |
| 本文献已被 CNKI 等数据库收录！ |
| 点击此处可从《江西师范大学学报(自然科学版)》浏览原始摘要信息 |
| 点击此处可从《江西师范大学学报(自然科学版)》下载免费的PDF全文 |
