CBMS Regional Conference in the Mathematical Sciences - "Finite Morse Index Solutions and Related Topics" -Winter 2007

CBMS 数学科学区域会议 - “有限莫尔斯指数解决方案和相关主题” - 2007 年冬季

• 批准号: 0628079
• 负责人: Shair Ahmad
• 金额: $ 3.28万
• 依托单位: University of Texas at San Antonio
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-03-01 至 2008-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0628079&HistoricalAwards=false
• 关键词: CBMS; Regional; Conference; Mathematical; Sciences

The lectures will involve boundary-value problems for nonlinear elliptic equations on bounded domains. They will encompass several important topics of current interest such as bifurcation theory, domain shape, Morse index solutions, and peak solutions; which occur in a great variety of applications of mathematics such as mathematical biology, catalysis theory, material science, and combustion. There will also be a discussion of interrelationships between these topics.The lectures will show a close connection between the theory of peak solutions and the theory of finite Morse index solutions. It is becoming increasingly apparent that finite Morse index solutions are very useful tools for studying nonlinear elliptic equations with rapid growth in the nonlinearity (faster than the critical growth). The talks will also include a number of interesting open problems that may be of interest to researchers in the area.

讲座将涉及有界域上非线性椭圆方程的边值问题。它们将涵盖当前感兴趣的几个重要主题，例如分岔理论、域形状、莫尔斯索引解和峰值解；它们出现在数学的各种应用中，例如数学生物学、催化理论、材料科学和燃烧。还将讨论这些主题之间的相互关系。讲座将展示峰值解理论与有限莫尔斯指数解理论之间的密切联系。越来越明显的是，有限莫尔斯指数解对于研究非线性快速增长（快于临界增长）的非线性椭圆方程来说是非常有用的工具。 会谈还将包括该领域研究人员可能感兴趣的一些有趣的开放性问题。