Mathematical Sciences: Critical Point Theory and Differential Equations

数学科学：临界点理论和微分方程

• 批准号: 9501132
• 负责人: Abbas Bahri
• 金额: $ 11.01万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501132&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Critical; Point; Theory

PI: Bahri DMS-9501132 Bahri will investigate questions arising in dynamical systems, nonlinear partial differential equations and geometry. These include collisions and existence of periodic orbits on 3-body type, the existence of infinitely many elliptic and infinitely many hyperbolic orbits on a given energy surface, the Weinstein conjecture and pseudo-orbits of contact forms, and the superlinear elliptic problem. Partial differential equations form a basis for mathematical modeling of the physical world. The role of mathematical analysis is not so much to create the equations as it is to provide qualitative and quantitative information about the solutions. This may include answers to questions about uniqueness, smoothness and growth. In addition, analysis often develops methods for approximation of solutions and estimates on the accuracy of these approximations.

PI：BHARRI DMS-9501132 BHURI将研究动力系统、非线性偏微分方程式和几何中出现的问题。这些问题包括三体型的碰撞和周期轨道的存在性，给定能量面上无穷多个椭圆轨道和无穷多个双曲轨道的存在，接触形式的Weinstein猜想和伪轨道，以及超线性椭圆问题。偏微分方程式是建立物理世界数学模型的基础。数学分析的作用与其说是创建方程，不如说是提供有关解的定性和定量信息。这可能包括回答有关唯一性、平稳性和成长性的问题。此外，分析经常开发出近似解的方法和对这些近似的精度的估计。