Mathematical Sciences: Some Semilinear Elliptic Problems

数学科学：一些半线性椭圆问题

• 批准号: 9622102
• 负责人: Zhi-Qiang Wang
• 金额: $ 6.83万
• 依托单位: Utah State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-06-01 至 2000-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622102&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Some; Semilinear; Elliptic

Abstract DMS-9622102 Wang This proposal is concerned with problems of the existence, qualitative properties, and multiplicity of solutions as well as bifurcation branches of solutions for some model equations of nonlinear elliptic problems including a nonlinear Neumann problem and a semilinear Schrodinger equation. Using these model equations we shall develop some general and systematic methods and approaches which can be used for more general problems. The proposal will use variational and topological techniques to develop analytical results for the problems concerned. Partial differential equations form a basis for mathematical modeling of the physical world. The problems in the proposal arise from a variety of areas of applied sciences. The role of mathematical analysis is to provide qualitative and quantitative information about the solutions, answering questions about uniqueness, multiplicity, shape and growth.

摘要DMS-9622102 WANG该提案与某些非线性椭圆问题的某些模型方程的解决方案的存在，定性特性和多样性有关，包括非线性椭圆形问题，包括非线性Neumann问题和半线性Schrodinger方程。使用这些模型方程式，我们将开发一些可以用于更通用问题的通用和系统的方法和方法。该提案将使用各种和拓扑技术来为有关问题开发分析结果。 部分微分方程构成了物理世界数学建模的基础。该提案中的问题来自多种应用科学领域。数学分析的作用是提供有关解决方案的定性和定量信息，回答有关唯一性，多样性，形状和成长的问题。