脉冲中立型时滞微分方程的正解的存在性

本文证明了线性脉冲中立型微分方程 [y(t)+p(t)y(t-τ)-r(t)y(t-ρ)]′+q(t)y(t-σ)=0,t≥0,t≠t_k, y(t_k~+)-y(t_k)=b_ky(t_k),k=1,2,…正解的存在性等价于一类非脉冲中立型方程正解的存在性,应用这一结果,建立了此类线性脉冲中立型微分方程正解存在性的若干充分条件。     

高阶非线性中立型时滞微分方程的渐近性态

本文研究一类高阶非线性中立型时滞微分方程解的渐近性态。这些结果推广了某些已知的结论。     

一类线性多步法关于变延迟非线性中立型微分方程的渐近稳定性

1引言中立型微分方程广泛出现于生物学、物理学及工程技术等诸多领域.数值求解中立型微分方程时,数值方法的稳定性研究具有无容置疑的重要性,其中渐近稳定性的研究是其重要组成部分.对于线性中立型延迟微分方程,渐近稳定性研究已有许多重要结果,如文献[1,2,3,4,5,6]等.对于非线性中立型变延迟微分方程,数值方法的稳定性研究近几年才有进展.2000年,Bellen等在文献[7]中讨论了Runge-Kutta法求解一类特殊的中立型延迟微分     

带强迫项高阶中立型微分方程的振动性和非振动性

我们给出一类强迫高阶非线性中立型时滞微分方程一切解振动的充分条件.而且,也研究了一类强迫一阶中立型方程非振动解的渐近性.     

具有分布时滞的二阶中立型微分方程的渐近性

我们考虑具有分布时滞的二阶中立型微分方程,给出了方程非振动解的渐近性质.     

中立型比例延迟微分系统线性θ-方法的渐近估计

本文研究了一类线性非自治中立型比例延迟微分系统线性θ-方法的渐近稳定性,并借助于泛函不等式得到了数值解的渐近估计.此渐近估计不仅比数值渐近稳定性描述得更加精确,而且还能给出非稳定情形数值解的上界估计式.数值算例验证了相关理论结果.     

一类具有无穷时滞中立型非稠定脉冲随机泛函微分方程积分解的存在性

本文讨论了一类具有无穷时滞中立型非稠定脉冲随机泛函微分方程,利用Sadovskii不动点原理等工具得到了其积分解的存在性,给出其在一类二阶无穷时滞中立型非稠定脉冲随机偏微分方程积分解的存在性中的应用.     

Asymptotic Properties of the Nonoscillatory Solutions of Second-Order Neutral Equations with a Deviating Argument

In the paper second-order linear neutral differential equations with a distributed delay are considered. The asymptotic properties of their nonoscillatory solutions are investigated.     

Some new integral inequalities and their applications in studying the stability of nonlinear integro-differential equations with time delay

In this paper, we generalize some integral inequalities to more general situations, and the inequalities of Pachpatte type are corollaries of our's. We establish bounds on the solutions, and we show the usefulness of our results in investigating the asymptotic behavior and the stability on the solutions of integral equations, differential equations and integro-differential equations with time delay.     

广义中立型系统的渐近稳定性及数值分析

１．引 言 考察如下广义中立型系统：其中,Ｌ,Ｍ,Ｎ ∈ Ｃｄ×ｄ为已知矩阵,　　　为已知向量值函数,　　　　　　　　　　当ｔ＞０时为未知函数,　　　　　　　　　　　　　　　　　　　　　　　　　为常数延时量． 对于　　　　　　　　　　　　　　　　　,１９６７年,Ｂｒａｙｔｏｎ［１］基于Ｌ,Ｍ,Ｎ为实对称矩阵,以及Ｉ± Ｎ和－Ｌ± Ｍ为正定矩阵时,讨论了（１）渐近稳定的充分条件;１９８４年,Ｊａｃｋｉｅｗｉｃｚ［２］基于 Ｌ,Ｍ,Ｎ为复系数时,研究了理论解的渐近稳定性及单步方法的数值稳定性;１９８８年,Ｂ…     

求解广义中立型系统的线性多步方法的NGP_G-稳定性

建立了广义中立型延迟系统理论解渐近稳定的充分条件 ,分析了用线性多步方法求解广义中立型延迟系统数值解的稳定性 ,在一定的Lagrange插值条件下 ,证明了数值求解广义中立型系统的线性多步方法NGPG_稳定的充分必要条件是线性多步方法是A_稳定的·     

脉冲强迫非线性时滞微分方程的渐近性

本文研究一类脉冲强迫非线性时滞微分方程的渐近性,所得结果不仅适用于线性方程和非线性方程,强迫方程和非强迫方程,脉冲方程和非脉冲方程,而且改进了最近文献［８］的主要结果．     

脉冲中立型时滞微分方程的振动性

证明了线性脉冲中立型时滞微分方程解的振动性等价于一类非脉冲中立型时滞微分方程解的振动性,应用这一结果建立了此类线性脉冲中立型微分方程解的振动性的显示判据。     

On the dominance of roots of characteristic equations for neutral functional differential equations

We present a sufficient condition for a zero of a function that arises typically as the characteristic equation of a linear functional differential equations of neutral type, to be simple and dominant. This knowledge is useful in order to derive the asymptotic behaviour of solutions of such equations. A simple characteristic equation, arisen from the study of delay equations with small delay, is analyzed in greater detail.     

无限时滞中立型随机泛函微分方程解的存在唯一性

有限时滞随机泛函微分方程的存在唯一性已经得到较多的研究,但对于无限时滞随机泛函微分方程的性质极少.本文在不需要线性增长条件,在一致Lipschitz条件下证明了无限时滞中立型随机泛函微分方程的存在唯一性,给出了精确解和近似解的误差估计,最后给出了解的矩估计.     

A generalization of the Haddock conjecture and its proof

In this paper, we study the asymptotic behavior of solutions for a class of neutral delay differential equations. These equations have important practical applications and generalize those on which Haddock conjectured that every solution of the equations tends to a constant. Our results improve the existing ones in the literature.     

Positivity and stability of linear functional differential equations with infinite delay

General linear functional differential equations with infinite delay are considered. We first give an explicit criterion for positivity of the solution semigroup of linear functional differential equations with infinite delay and then a Perron‐Frobenius type theorem for positive equations. Next, a novel criterion for the exponential asymptotic stability of positive equations is presented. Furthermore, two sufficient conditions for the exponential asymptotic stability of positive equations subjected to structured perturbations and affine perturbations are provided. Finally, we applied the obtained results to problems of the exponential asymptotic stability of Volterra integrodifferential equations. To the best of our knowledge, most of the results of this paper are new.     

Convergence of discrete analogues of a generalization of J.R. Haddock’s conjecture

This work focuses on the asymptotic behavior of solutions for a class of neutral delay difference equations, which are discrete analogues of a generalization of J.R. Haddock’s conjecture. It is shown that every bounded solution of the equations converges to a constant. Our results improve some known results from the literature.     

Asymptotic Behavior of Forced Nonlinear Delay Differential Equations with Impulses

The purpose of this paper is to investigate the asymptotic behavior of solutions of the forced nonlinear delay differential equations with impulses Our results, which hold for linear and nonlinear equations, forced and unforced equations, impulsive and nonimpulsive equations, improve and generalize the known results recently obtained in [8]. Received September 7, 1997, Revised May 26, 1998, Accepted July 15, 1998     

On the logistic delay differential equations with piecewise constant argument and quasi-periodic time dependence

In this paper, we discuss the quasi-periodic logistic delay differential equations. As a corollary, we give a more sharp result than that in [G. Seifert, J. Differential Equations 164 (2000) 451-458] for the periodic logistic delay differential equations.