几类三阶中立型微分方程的振动性与渐近性研究
发布时间：2018-11-25 15:53
【摘要】：微分方程的振动性理论是微分方程理论中一个十分重要的分支，它具有非常深刻的实际背景.本文利用算子方法、Riccati变换、函数平均值和积分不等式等方法对几类微分方程作进一步的研究,得到了若干新的结果.根据内容本文分为五章.第一章绪论,介绍本文研究的主要问题及其背景.第二章主要利用算子方法研究了三阶中立型微分方程的振动性定理,其中t≥t0.且α≥1是两个正奇数的比值,得到了若干保证方程所有解振动的充分条件,推广了Tian et al的结果,并给出例子来说明所得结果的应用.第三章主要研究了具有分布时滞的三阶中立型微分方程的振动性与渐近性,其中α≥1是两个正奇数的比值,得到了两个保证方程所有解振动或者趋于零的充分条件,改进了Tian et al的结果,推广了Zhang et al的结果,并给出例子来说明所得结果的应用.第四章利用广义Riccati变换研究了三阶中立型微分方程的振动性与渐近性,其中t≥t0,且α≥1是两个正奇数的比值,得到了保证方程所有解振动或者趋于零的充分条件,推广了本文第三章的结果.并给出两个例子加以说明.第五章主要研究了三阶中立型分布时滞微分方程的振动定理,其中a≥1是两个正奇数的比值,且得到了两个保证方程一切解振动的充分条件.推广了本文第三章的结果，并给出一个例子加以说明.
[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，
本文编号：2356665
[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，
本文编号：2356665
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