一类高阶中立型泛函微分方程渐近行为的研究
发布时间：2019-02-16 17:44
【摘要】：泛函微分方程的定性理论,是描述人类社会发展规律的有效工具.近几十年,在力学、生物数学、经济数学、通讯理论等众多领域中都提出了由微分方程理论描述的具体数学模型.而泛函微分方程的振动理论,作为泛函微分方程定性理论的一个重要部分,对其进行深入的研究不仅具有重大的理论意义,而且对于人类社会发展具有一定的实际意义.在本篇硕士论文中,我们研究如下一类高阶中立型泛函微分方程的振动行为：第一章简要地概述了泛函微分方程振动性问题的发展背景及国内外研究现状;第二章介绍了泛函微分方程的振动性的相关定义,及证明振动性所需要的重要定理及不等式;第三章讨论了n阶(n≥3)中立型微分方程的振动行为,在β=1与β≠1两种不同情形下获得了方程非振动解x(t)的渐近行为,并运用广义的Riccati变换,Philos型积分平均技术,Young不等式,Schwarz不等式、H(?)lder不等式等理论与方法,获得了方程的解振动的新的判据,推广并改进了已有文献的结果.
[Abstract]:The qualitative theory of functional differential equation is an effective tool to describe the law of human social development. In recent decades, in many fields such as mechanics, biology mathematics, economic mathematics, communication theory and so on, the concrete mathematical model described by the theory of differential equation has been put forward. As an important part of the qualitative theory of functional differential equations, the vibration theory of functional differential equations has not only great theoretical significance, but also practical significance for the development of human society. In this thesis, we study the oscillatory behavior of a class of higher order neutral functional differential equations: in Chapter 1, the development background of Oscillation of functional differential equations and the current research situation at home and abroad are briefly summarized. The second chapter introduces the definition of Oscillation of functional differential equations and the important theorems and inequalities needed to prove Oscillation. In chapter 3, the oscillatory behavior of neutral differential equation of n order (n 鈮，
本文编号：2424689
[Abstract]:The qualitative theory of functional differential equation is an effective tool to describe the law of human social development. In recent decades, in many fields such as mechanics, biology mathematics, economic mathematics, communication theory and so on, the concrete mathematical model described by the theory of differential equation has been put forward. As an important part of the qualitative theory of functional differential equations, the vibration theory of functional differential equations has not only great theoretical significance, but also practical significance for the development of human society. In this thesis, we study the oscillatory behavior of a class of higher order neutral functional differential equations: in Chapter 1, the development background of Oscillation of functional differential equations and the current research situation at home and abroad are briefly summarized. The second chapter introduces the definition of Oscillation of functional differential equations and the important theorems and inequalities needed to prove Oscillation. In chapter 3, the oscillatory behavior of neutral differential equation of n order (n 鈮，
本文编号：2424689
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