【摘要】：隨著現(xiàn)代社會的發(fā)展,對常微分方程性質(zhì)的研究逐步成為數(shù)學(xué)領(lǐng)域的研究熱點(diǎn)之一.中立型微分方程通常產(chǎn)生于自然科學(xué)與工程領(lǐng)域,因?yàn)樗芎芎玫孛枋鲎匀唤缰械母鞣N復(fù)雜現(xiàn)象,一直以來受到大量科研工作者的廣泛關(guān)注.近年來,帶有時(shí)滯的微分方程和非線性的微分方程逐步受到重視.但是到目前,關(guān)于多時(shí)滯的中立型微分方程的性質(zhì)的研究結(jié)果還不多.基于上述情況,本文對幾類多時(shí)滯中立型微分方程的振動性進(jìn)行了深入研究.本文分為四章.第一章是緒論部分,主要介紹了部分學(xué)者的研究工作以及本文所要研究的主要內(nèi)容.第二章主要討論了二階多時(shí)滯中立型微分方程的振動性.其中r(t)0且r(t)∈C1([t0,∞))利用比較原理將二階多時(shí)滯中立型微分方程的振動性判斷轉(zhuǎn)化為判斷一階方程的振動性,這種比較原理最大程度的使我們研究的二階方程得到簡化.第三章主要討論了二階多時(shí)滯非線性中立型微分方程的振動性.其中γ和β是兩個(gè)正奇數(shù)的比,a(t)0且a(t)∈C'([t0,∞)).由一階多時(shí)滯中立型微分不等式解的情況判斷所研究的二階非線性方程的振動性.第四章主要討論了三階多時(shí)滯中立型微分方程的振動性.其中γ是兩個(gè)正奇數(shù)的比,a(t)0且a(t)∈C'([t0,∞)).由一個(gè)積分不等式判斷三階多時(shí)滯中立型微分方程的振動性.第二章,第三章中研究的兩個(gè)方程,都滿足且Ti(t)0,σj(t)0,同時(shí)還滿足limt→∞Ti(t)= ∞,limt→∞(t)=∞,Υi'(￡)≥Υ0,Υi○σj=σj○Υi.第四章研究的方程中,pi(t)滿足0≤pi(t)≤p1,且這里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).
【學(xué)位授予單位】：山西大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O175

【共引文獻(xiàn)】

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本文編號：2130453