【摘要】：泛函微分方程的定性理論,是描述人類社會(huì)發(fā)展規(guī)律的有效工具.近幾十年,在力學(xué)、生物數(shù)學(xué)、經(jīng)濟(jì)數(shù)學(xué)、通訊理論等眾多領(lǐng)域中都提出了由微分方程理論描述的具體數(shù)學(xué)模型.而泛函微分方程的振動(dòng)理論,作為泛函微分方程定性理論的一個(gè)重要部分,對(duì)其進(jìn)行深入的研究不僅具有重大的理論意義,而且對(duì)于人類社會(huì)發(fā)展具有一定的實(shí)際意義.在本篇碩士論文中,我們研究如下一類高階中立型泛函微分方程的振動(dòng)行為：第一章簡要地概述了泛函微分方程振動(dòng)性問題的發(fā)展背景及國內(nèi)外研究現(xiàn)狀;第二章介紹了泛函微分方程的振動(dòng)性的相關(guān)定義,及證明振動(dòng)性所需要的重要定理及不等式;第三章討論了n階(n≥3)中立型微分方程的振動(dòng)行為,在β=1與β≠1兩種不同情形下獲得了方程非振動(dòng)解x(t)的漸近行為,并運(yùn)用廣義的Riccati變換,Philos型積分平均技術(shù),Young不等式,Schwarz不等式、H(?)lder不等式等理論與方法,獲得了方程的解振動(dòng)的新的判據(jù),推廣并改進(jìn)了已有文獻(xiàn)的結(jié)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，

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