【摘要】：本文主要討論了高階非線性具有偏差變元的微分積分方程解的有界性。根據(jù)內(nèi)容本論文分為以下三章:第一章.主要介紹了問題研究的歷史背景和該領(lǐng)域的研究現(xiàn)狀。第二章.在這一章中,利用新建立的積分不等式,在適當(dāng)?shù)募僭O(shè)條件下討論了一類高階非線性具有偏差變元的微分積分方程解的有界性,得到如下結(jié)果定理2.3.1設(shè)fv(t),gj(t),ki(t)和P(t)是定義在[a,∞)上的正的連續(xù)函數(shù),v=1,2.…l,j =1,2,... = 1,2,...m.(?)(t)是連續(xù)可微函數(shù)且滿足(?)(t)≤t,(?)'(t)0. limt→∞(?)(t)a.rv:qj,Pi∈(0,1]是常數(shù),且有若還設(shè)成立,則對于定義在[r,a]上的任意一個初始函數(shù)θ(t),方程(2.1.1)存在一個定義在[r, a] ∪[a, ∞)上的且滿足初始條件x(t)=θ(t),t∈[r, a]的解x(t),D0(x;p0)(t)在[a, ∞)是有界的。定理2.3.2設(shè)F(f,x,y)同定理1,且除了條件(3.1.3)(3.1.4)(3.1.5)外還滿足則對于方程(2.1.1)的每一個解x(t),都有D0(x;p0)(t)當(dāng)t→∞時,有有限極限。特別地,對(2.1.1)的任一個振動解x(t),D0(x;p0)(t)當(dāng)t→∞時趨于0.第三章.在這一章中,在適當(dāng)?shù)臈l件下利用不等式討論了一類具有偏差變元的微分積分方程解的有界性,得到如下結(jié)果定理3.3.1假設(shè)g(t)≤t且qi(t)是正的連續(xù)函數(shù),0≤i≤n,ψ(t)在[a,∞),wi(u)∈F,0≤i≤n-1,則且假設(shè)除此之外還有則方程(3.1.2)的每一個解x(t)滿足Lkx(t)=O(Jn-k-1(t)),t→∞,k=0,1,2,...,n-1.定理3.3.2.假設(shè)g(t)≤t且qi(t)是正的連續(xù)函數(shù),0≤i≤n,ψ(t)在[a,∞),wi(u)∈F,0≤i≤n-1,則且除此之外假設(shè)1≤i≤n-1.則方程(3.1.2)的解x(t)滿足Lkx(t)→0,0≤k≤n-1.
[Abstract]:In this paper, we mainly discuss the boundedness of the solution of the differential integral equation with deviation argument. According to the content of this paper is divided into the following three chapters: the first chapter. This paper mainly introduces the historical background of the problem research and the present situation of the research in this field. Chapter 2 In this chapter, the boundedness of the solutions of a class of higher order nonlinear differential integral equations with deviated arguments is discussed under appropriate assumptions by using the newly established integral inequalities. We obtain the following theorem 2.3.1 Let fv (t) GJ (t) (t) and P (t) be positive continuous functions defined on [a, 鈭，

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