泛函微分方程论文：两类高阶具偏差变元微分方程周期解的存在性.doc

泛函微分方程论文：两类高阶具偏差变元微分方程周期解的存在性【中文摘要】泛函微分方程是描述带有时滞现象的一种数学模型。带有周期时滞的泛函微分方程在生物学、经济学、生态学和自动控制等实际问题中有着广泛的应用。因此,对带有周期时滞的泛函微分方程周期解的存在性的研究具有重要的现实意义。因而,研究泛函微分方程周期解问题,不仅有很大的应用价值,而且还丰富了泛函微分方程的理论体系。本文主要讨论了两类泛函微分方程的周期解的存在性问题。在第一章中,简述了泛函微分方程周期解问题的历史背景以及已有的研究成果,重点综述了本文的研究工作。在第二章中,我们研究了一类二阶具多偏差变元的泛函微分方程周期解的存在性,利用重合度理论和关于周期函数的最佳不等式,得到了文中的若干结论。在第三章中,研究了一类三阶具偏差变元的泛函微分方程的周期解的存在性,得到了文中的若干结论。【英文摘要】Functional differential equation is a mathematical model describing the phenomenon with time delays. The functional differential equations with periodic delays represent a natural framework for mathematical modeling of many real world phenomena such as biology, economy, ecology, automatic control and so on. Therefore, the researches on existence of periodic solutions for functional differential equations with periodic delays have practical significance.Furthermore, investigating periodic solution problem for functional differential equation not only has applied value but also enriches the system of functional differential equation.This thesis mainly studies the periodic solution problem for functional differential equations, as following:In chapter, the background of the subjects relevant to this dissertation is introduced. Then, the known progress on study of functional differential equation and the main results of the thesis are introduced.In chapter, we study a kind of periodic solutions of the second order differential equation with multiple deviating arguments is investigated.By means of Mawhin continue theorem and sharp inequalities for periodic functions, some sufficient conditions are obtained.In chapter, we study a kind of third order functional differential equation with a deviating argument is investigated. Sufficient conditions for the existence of periodic solutions are obtained.【关键词】泛函微分方程 偏差变元 周期解 重合度【英文关键词】Functional Differential Equations Deviating Periodic Solution Coincidence Degree【目录】两类高阶具偏差变元微分方程周期解的存在性摘要3-4ABSTRACT4第一章 前言6-9第二章 一类二阶具多偏差变元微分方程的周期解9-202.1 引言9-102.2 相关条件