Mathematical Sciences: Monotonicity in Differential Equations

数学科学：微分方程的单调性

• 批准号: 9002431
• 负责人: John Haddock
• 金额: $ 1.29万
• 依托单位: University of Memphis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-15 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002431&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Monotonicity; Differential; Equations

This project supports mathematical research on problems arising in the study of dynamical systems and differential equations. The equations are functional differential equations of retarded type. In certain equations occurring in biological models, the retardation of memory effect is a natural feature. Work will focus on four main topics. The first concerns monotone flows on monotone dynamical systems. Efforts to modify standard systems theory to present a unified treatment of differential equations for which the set of equilibrium points contains all (phase space) constant functions will be made. The second topic relates to instability of physical systems. Applications of invariance principles of finite delay equations will be made to obtain instability results for finite and infinite delay functional differential equations. Instability is characterized by the property that all solutions passing near an unstable point must leave every neighborhood of the point. Neutral functional differential equations make up the third element of this project. Work will be done in establishing comparison-convergence techniques for approximating solutions. The final goal of the research is that of using monotone iteration techniques to study periodic boundary value problems for functional differential equations. Both the existence of periodic solutions and techniques for constructing them will be considered.

该项目支持对动力系统和微分方程研究中出现的问题进行数学研究。 这些方程是延迟型函数微分方程。 在生物模型中出现的某些方程中，记忆效应的延迟是一个自然特征。 工作将集中在四个主要主题上。 第一个涉及单调动力系统上的单调流。 将努力修改标准系统理论，以提出微分方程的统一处理，其中平衡点集包含所有（相空间）常数函数。 第二个主题涉及物理系统的不稳定性。 应用有限时滞方程的不变性原理来获得有限和无限时滞泛函微分方程的不稳定性结果。 不稳定的特点是所有在不稳定点附近通过的解都必须离开该点的每个邻域。 中性泛函微分方程构成了该项目的第三个要素。 将致力于建立用于近似解决方案的比较收敛技术。 研究的最终目标是利用单调迭代技术研究泛函微分方程的周期边值问题。 将考虑周期解的存在性和构造它们的技术。