Mathematical Sciences: Monotonicity in Differential Equations

这个项目支持数学研究的问题 在动力系统和微分学的研究中产生的 方程 方程是泛函微分方程 弱智类型。 在生物学中的某些方程式中， 模型，记忆效应的延迟是一个自然的特征。 工作将侧重于四个主要专题。 第一个问题涉及 单调动力系统上的单调流 努力修订 标准系统理论提出了一个统一的处理 微分方程的平衡点集 包含所有（相空间）常数函数。 的 第二个主题涉及物理系统的不稳定性。 有限时滞方程不变性原理的应用 将获得有限的不稳定性结果， 无穷时滞泛函微分方程 不稳定是 其特征在于，所有的解决方案，通过附近的一个 不稳定点必须离开该点的每个邻域。 第三类是中立型泛函微分方程 这个项目的元素。 将开展工作， 近似解的比较收敛技术。 研究的最终目的是使用单调 研究周期边值问题的迭代方法 泛函微分方程。 无论是存在 周期解和构造它们的技术将是 考虑了

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.