Mathematical Sciences: Nonlinear Elliptic Boundary Value Problems

数学科学：非线性椭圆边值问题

• 批准号: 9103851
• 负责人: Martin Schechter
• 金额: $ 8.49万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103851&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Elliptic; Boundary

This project will study the solvability of nonlinear elliptic boundary value problems. Main emphasis will be placed in the cases where either the problem is semilinear but the spectrum of the linear part is not known, or the nonlinear part interferes with the spectrum. Recent developments on abstractions of the mountain pass lemma are expected to render information on the issue of existence and multiplicity of solutions for these problems. The problems to be studied are basic questions arising in equations that model problems in areas such as mathematical physics, biomathematics, and chemistry.

本课题将研究非线性椭圆型边值问题的可解性。重点将放在问题是半线性的情况下，但线性部分的频谱是未知的，或者非线性部分干扰了频谱。关于山口引理抽象的最新进展有望提供有关这些问题的解的存在性和多重性问题的信息。要研究的问题是在数学物理、生物数学和化学等领域中建模问题的方程中出现的基本问题。