一类高阶非线性具有偏差变元的微分积分方程解的有界性研究

发布时间：2018-07-17 00:54

【摘要】：本文主要讨论了高阶非线性具有偏差变元的微分积分方程解的有界性。根据内容本论文分为以下三章:第一章.主要介绍了问题研究的历史背景和该领域的研究现状。第二章.在这一章中,利用新建立的积分不等式,在适当的假设条件下讨论了一类高阶非线性具有偏差变元的微分积分方程解的有界性,得到如下结果定理2.3.1设fv(t),gj(t),ki(t)和P(t)是定义在[a,∞)上的正的连续函数,v=1,2.…l,j =1,2,... = 1,2,...m.(?)(t)是连续可微函数且满足(?)(t)≤t,(?)'(t)0. limt→∞(?)(t)a.rv:qj,Pi∈(0,1]是常数,且有若还设成立,则对于定义在[r,a]上的任意一个初始函数θ(t),方程(2.1.1)存在一个定义在[r, a] ∪[a, ∞)上的且满足初始条件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设F(f,x,y)同定理1,且除了条件(3.1.3)(3.1.4)(3.1.5)外还满足则对于方程(2.1.1)的每一个解x(t),都有D0(x;p0)(t)当t→∞时,有有限极限。特别地,对(2.1.1)的任一个振动解x(t),D0(x;p0)(t)当t→∞时趋于0.第三章.在这一章中,在适当的条件下利用不等式讨论了一类具有偏差变元的微分积分方程解的有界性,得到如下结果定理3.3.1假设g(t)≤t且qi(t)是正的连续函数,0≤i≤n,ψ(t)在[a,∞),wi(u)∈F,0≤i≤n-1,则且假设除此之外还有则方程(3.1.2)的每一个解x(t)满足Lkx(t)=O(Jn-k-1(t)),t→∞,k=0,1,2,...,n-1.定理3.3.2.假设g(t)≤t且qi(t)是正的连续函数,0≤i≤n,ψ(t)在[a,∞),wi(u)∈F,0≤i≤n-1,则且除此之外假设1≤i≤n-1.则方程(3.1.2)的解x(t)满足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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