多时滞中立型微分方程的振动性
发布时间：2018-07-17 17:47
【摘要】：随着现代社会的发展,对常微分方程性质的研究逐步成为数学领域的研究热点之一.中立型微分方程通常产生于自然科学与工程领域,因为它能很好地描述自然界中的各种复杂现象,一直以来受到大量科研工作者的广泛关注.近年来,带有时滞的微分方程和非线性的微分方程逐步受到重视.但是到目前,关于多时滞的中立型微分方程的性质的研究结果还不多.基于上述情况,本文对几类多时滞中立型微分方程的振动性进行了深入研究.本文分为四章.第一章是绪论部分,主要介绍了部分学者的研究工作以及本文所要研究的主要内容.第二章主要讨论了二阶多时滞中立型微分方程的振动性.其中r(t)0且r(t)∈C1([t0,∞))利用比较原理将二阶多时滞中立型微分方程的振动性判断转化为判断一阶方程的振动性,这种比较原理最大程度的使我们研究的二阶方程得到简化.第三章主要讨论了二阶多时滞非线性中立型微分方程的振动性.其中γ和β是两个正奇数的比,a(t)0且a(t)∈C'([t0,∞)).由一阶多时滞中立型微分不等式解的情况判断所研究的二阶非线性方程的振动性.第四章主要讨论了三阶多时滞中立型微分方程的振动性.其中γ是两个正奇数的比,a(t)0且a(t)∈C'([t0,∞)).由一个积分不等式判断三阶多时滞中立型微分方程的振动性.第二章,第三章中研究的两个方程,都满足且Ti(t)0,σj(t)0,同时还满足limt→∞Ti(t)= ∞,limt→∞(t)=∞,Υi'(￡)≥Υ0,Υi○σj=σj○Υi.第四章研究的方程中,pi(t)满足0≤pi(t)≤p1,且这里i∈{1,2,…,m},j∈{1,2,…,n).
[Abstract]:With the development of modern society, the study of the properties of ordinary differential equations has gradually become one of the hotspots in the field of mathematics. Neutral differential equations are usually produced in the field of natural science and engineering. Because it can describe the complex phenomena in nature well, it has been widely concerned by a large number of researchers. The differential equation with time delay and the nonlinear differential equation are gradually paid attention. But at present, there are not many research results on the properties of Neutral Differential Equations with multiple delays. Based on the above situation, the vibration of several classes of Neutral Differential Equations with multiple delays is deeply studied. This paper is divided into four chapters. The first chapter is the introduction Part of this paper mainly introduces the research work of some scholars and the main contents of this paper. The second chapter mainly discusses the oscillation of two order neutral differential equations with multiple delay. In which R (T) 0 and R (T) C1 ([t0, infinity)) use the comparison principle to convert the vibration judgment of the two order neutral differential equation to the first order equation. This comparison principle simplifies the two order equation of our study to the maximum extent. The third chapter mainly discusses the oscillation of two order multi delay nonlinear neutral differential equations. Among them, the ratio of gamma and beta to two positive odd numbers, a (T) 0 and a (T) C'([t0, infinity)). The oscillation of the two order nonlinear equations studied. The fourth chapter mainly discusses the oscillation of three order neutral differential equations with multiple delays. Among them, the ratio of two positive odd numbers, a (T) 0 and a (T) C'([t0, infinity)). The oscillation of the neutral differential equation of the three order multi delay is judged by an integral inequality. Second chapter, two in the third chapter. Ti (T) 0, sigma J (T) 0, and also satisfy limt, Ti (T) = ~ (T) =, limt, infinity (T) = =, I'() > > 0, I > j= sigma fourth. M}, J {1,2,... N).
【学位授予单位】：山西大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175
本文编号：2130453
[Abstract]:With the development of modern society, the study of the properties of ordinary differential equations has gradually become one of the hotspots in the field of mathematics. Neutral differential equations are usually produced in the field of natural science and engineering. Because it can describe the complex phenomena in nature well, it has been widely concerned by a large number of researchers. The differential equation with time delay and the nonlinear differential equation are gradually paid attention. But at present, there are not many research results on the properties of Neutral Differential Equations with multiple delays. Based on the above situation, the vibration of several classes of Neutral Differential Equations with multiple delays is deeply studied. This paper is divided into four chapters. The first chapter is the introduction Part of this paper mainly introduces the research work of some scholars and the main contents of this paper. The second chapter mainly discusses the oscillation of two order neutral differential equations with multiple delay. In which R (T) 0 and R (T) C1 ([t0, infinity)) use the comparison principle to convert the vibration judgment of the two order neutral differential equation to the first order equation. This comparison principle simplifies the two order equation of our study to the maximum extent. The third chapter mainly discusses the oscillation of two order multi delay nonlinear neutral differential equations. Among them, the ratio of gamma and beta to two positive odd numbers, a (T) 0 and a (T) C'([t0, infinity)). The oscillation of the two order nonlinear equations studied. The fourth chapter mainly discusses the oscillation of three order neutral differential equations with multiple delays. Among them, the ratio of two positive odd numbers, a (T) 0 and a (T) C'([t0, infinity)). The oscillation of the neutral differential equation of the three order multi delay is judged by an integral inequality. Second chapter, two in the third chapter. Ti (T) 0, sigma J (T) 0, and also satisfy limt, Ti (T) = ~ (T) =, limt, infinity (T) = =, I'() > > 0, I > j= sigma fourth. M}, J {1,2,... N).
【学位授予单位】：山西大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175
【共引文献】
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1 仉志余;王晓霞;俞元洪;;三阶中立型分布时滞微分方程的振动定理[J];工程数学学报;2013年06期
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相关博士学位论文 前1条
1 李同兴;几类高阶时滞微分方程的定性分析[D];山东大学;2013年
相关硕士学位论文 前6条
1 谷军华;几类微分方程的振动性研究[D];曲阜师范大学;2012年
2 蔡宏铮;两类高阶非线性带阻尼项泛函微分方程的振动性与渐近性[D];广东技术师范学院;2013年
3 张言军;两类三阶非线性时滞动力方程解的振动性[D];曲阜师范大学;2013年
4 孙逢垒;三阶微分方程解的振动性[D];曲阜师范大学;2013年
5 李晶晶;两类微分方程解的定性分析[D];安徽大学;2014年
6 裴晓帅;三阶泛函微分方程的振动性[D];山西大学;2012年
，本文编号：2130453
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