Mathematical Sciences: Schrodinger Operators and Elliptic Eigenvalue Problems with an Indefinite Weight Function

数学科学：薛定谔算子和具有不定权函数的椭圆特征值问题

• 批准号: 8703138
• 负责人: Michel Lapidus
• 金额: $ 4.26万
• 依托单位: University of Georgia Research Foundation Inc
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8703138&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Schrodinger; Operators; Elliptic

This research treats spectral theory of Schrodinger operators and elliptic boundary value problems with indefinite weight functions. Such eigenvalue problems occur naturally in the study of nonlinear partial differential equations and are of broad interest in mathematical physics and applied mathematics. In physics and engineering they arise, for instance, in transport theory, lasers, crystal coloration, hydrodynamics, and reaction-diffusion. Professor Lapidus will conduct research on semilinear elliptic equations and the related topic of eigenvalue problems with indefinite weight. The elliptic problems are set on bounded domains with Dirichlet or Neumann boundary conditions. He will also consider Schrodinger operators on unbounded domains with discrete spectrum. He will investigate both eigenvalues and eigenfunctions, with special emphasis on extensions of classical asymptotic formulas and remainder estimates, distribution of eigenvalues, inverse problems, and decay and oscillation of the eigenfunctions.

本研究将薛定谔的光谱理论 算子与不定椭圆边值问题 权重函数 这样的特征值问题自然发生在 非线性偏微分方程研究， 对数学物理和应用数学有广泛的兴趣。 在物理学和工程学中，它们出现在交通运输等领域 理论，激光，晶体着色，流体力学，和 反应扩散 拉皮德斯教授将进行半线性的研究 椭圆型方程及其特征值问题 不确定的重量。 椭圆型问题是在有界 Dirichlet或Neumann边界条件。 他将 也考虑无界域上的薛定谔算子， 离散谱 他将研究特征值和 本征函数，特别强调经典的扩展 渐近公式和余项估计，分布 特征值，逆问题，以及衰减和振荡的 本征函数