【摘要】：微分方程的振動(dòng)性理論是微分方程理論中一個(gè)十分重要的分支，它具有非常深刻的實(shí)際背景.本文利用算子方法、Riccati變換、函數(shù)平均值和積分不等式等方法對(duì)幾類微分方程作進(jìn)一步的研究,得到了若干新的結(jié)果.根據(jù)內(nèi)容本文分為五章.第一章緒論,介紹本文研究的主要問題及其背景.第二章主要利用算子方法研究了三階中立型微分方程的振動(dòng)性定理,其中t≥t0.且α≥1是兩個(gè)正奇數(shù)的比值,得到了若干保證方程所有解振動(dòng)的充分條件,推廣了Tian et al的結(jié)果,并給出例子來說明所得結(jié)果的應(yīng)用.第三章主要研究了具有分布時(shí)滯的三階中立型微分方程的振動(dòng)性與漸近性,其中α≥1是兩個(gè)正奇數(shù)的比值,得到了兩個(gè)保證方程所有解振動(dòng)或者趨于零的充分條件,改進(jìn)了Tian et al的結(jié)果,推廣了Zhang et al的結(jié)果,并給出例子來說明所得結(jié)果的應(yīng)用.第四章利用廣義Riccati變換研究了三階中立型微分方程的振動(dòng)性與漸近性,其中t≥t0,且α≥1是兩個(gè)正奇數(shù)的比值,得到了保證方程所有解振動(dòng)或者趨于零的充分條件,推廣了本文第三章的結(jié)果.并給出兩個(gè)例子加以說明.第五章主要研究了三階中立型分布時(shí)滯微分方程的振動(dòng)定理,其中a≥1是兩個(gè)正奇數(shù)的比值,且得到了兩個(gè)保證方程一切解振動(dòng)的充分條件.推廣了本文第三章的結(jié)果，并給出一個(gè)例子加以說明.
[Abstract]:Oscillation theory of differential equations is a very important branch of differential equation theory, which has a very deep practical background. In this paper, some differential equations are further studied by means of operator method, Riccati transform, function mean value and integral inequality, and some new results are obtained. According to the content of this paper is divided into five chapters. The first chapter introduces the main problems and background of this paper. In chapter 2, the oscillatory theorems of third-order neutral differential equations are studied by means of operator method, where t 鈮，

本文編號(hào)：2356665