泛函微分方程论文泛函微分方程周期解问题的若干研究.docVIP

泛函微分方程论文：泛函微分方程周期解问题的若干研究 【中文摘要】严格地说,在现实生活和生产中时滞是不可避免的,即使以光速传播的信息系统也不例外。在这个意义下,在建立数学模型时,略去滞量便达不到必要的精确度甚至导致错误的模型。因此,对泛函微分方程的研究不仅具有重要的理论价值而且具有重要的现实意义。本文就几类泛函微分方程正解或周期解的存在性问题进行了一些探论,并得出了一些结论。全文共分为五章。在第一章中,简述泛函微分方程的历史背景和已有的科研成果,重点综述本文的研究工作。在第二章中,研究了两类带有有限时滞和无界分布时滞泛函微分方程,通过利用Banach压缩映像原理,我们获得了这两类方程存在正解的一些充分条件。在第三章中,利用重合度理论研究了一类泛函微分方程周期解的存在性,得到了该方程存在周期解的充分条件。此外,给出了一个实例说明结果是可行。在第四章中,通过利用Krasnoselskii不动点定理、Banach压缩映像原理、矩阵测度及分析技巧,我们研究了带分布时滞和离散时滞泛函微分方程周期解的存在性。此外,给出了一个实例说明结果的应用。在第五章中,利用Manasevich-Mawhin延拓定理和一些分析技巧,获得了带多个p-Laplacian算子Duffing型方程存在周期解的充分性定理。此外,通过运用举例来说明了此定理的有效性的。 【英文摘要】Strictly speaking, in real life and production delay is inevitable, Even if information systems by transmitted at the speed of light is no exception. In this sense, the mathe-matical model, omitting delay is then not reach the necessary precision and even cause an error model. Therefore, the researches on functional differential equation have important theoretic value and practical significance.In this paper, the existence of the positive solutions or periodic solutions of several functional differential equations are discussed, many important results are also given in it. Full text is divided into five chapters.In the first Chapter, brief historical background and existing research of functional differential equations, focusing on the work of this study reviewed.In the second Chapter, we study two types of neutral functional differential equations with, finite or unbounded distributed deviating arguments. By using Banach contraction principle, we obtain some sufficient conditions for the existence of positive solutions to these equations.In ChapterⅢ, using Mawhin’s coincidence degree theory, the existence of the periodic solution of fourth-order differential equations are studied. Moreover, we construct an example to illustrate the feasibility of our results.In ChapterⅣ, using Krasnoselskii’s fixed point theorem, Banach contraction prin-ciple, matrix measure and functional analysis methods, we stu