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。     

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。     

高阶脉冲中立型偏泛函微分方程的强迫振动性

研究一类具高阶Laplace算子的高阶脉冲非线性中立型偏泛函微分方程的强迫振动性,利用Green公式和微分不等式方法将所讨论的脉冲中立型偏微分方程转化为脉冲中立型微分不等式的问题,获得了这类方程在三类不同边值条件下所有解强迫振动的若干充分条件.     

On abstract degenerate neutral differential equations

We introduce a new abstract model of functional differential equations, which we call abstract degenerate neutral differential equations, and we study the existence of strict solutions. The class of problems and the technical approach introduced in this paper allow us to generalize and extend recent results on abstract neutral differential equations. Some examples on nonlinear partial neutral differential equations are presented.     

中立型随机泛函微分方程的Khasminskii型定理

本文对中立型随机泛函微分方程建立了Khasminskii型定理,这个定理显示在局部Lipschitz条件但是不要求线性增长的条件下,中立型随机泛函微分方程存在一个全局解.本文的这个解存在性条件可以包含更广的一类非线性中立型随机泛函微分方程.最后,本文给出一个例子来阐述我们的思想.     

Oscillation and stability of nonlinear neutral impulsive delay differential equations

In this paper, oscillation and stability of nonlinear neutral impulsive delay differential equation are studied. The main result of this paper is that oscillation and stability of nonlinear impulsive neutral delay differential equation are equivalent to oscillation and stability of corresponding nonimpulsive neutral delay differential equations. At last, two examples are given to illustrate the importance of this study.     

Linearized oscillations for higher order neutral differential equations

In this paper, the oscillation of certain nonlinear neutral differential equations has been studied with the help of the oscillation of associated linear neutral differential equations     

非线性中立型泛函微分方程Runge-Kutta 法的稳定性和收敛性

本文涉及Runge-Kutta 法变步长求解非线性中立型泛函微分方程(NFDEs) 的稳定性和收敛性.为此, 基于Volterra 泛函微分方程Runge-Kutta 方法的B- 理论, 引入了中立型泛函微分方程Runge-Kutta 方法的EB (expanded B-theory)-稳定性和EB-收敛性概念. 之后获得了Runge-Kutta 方法变步长求解此类方程的EB - 稳定性和EB- 收敛性. 这些结果对中立型延迟微分方程和中立型延迟积分微分方程也是新的.     

中立型泛函微分方程的周期解

对于中立型泛函微分方程,证明了解的毕竟有界性蕴含周期解的存在性,把常微分方程中著名的Yoshizawa周期解存在定理推广到中立型泛函微分方程,然后利用所得结果给出一类产生于电力系统的中立型时滞泛函微分方程周期解存在惟一与吸引的条件。     

On a new class of abstract neutral differential equations

In this work we introduce a new class of abstract neutral differential equations and study the existence of mild and strict solutions. Some concrete applications involving partial neutral differential equations are considered.     

RAZUMIKHIN-TYPE THEOREM FOR NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.     

随机中立型泛函微分方程的稳定性态

给出了一类中立型随机泛函方程的随机一致稳定性的充分条件,利用了新的分析技巧处理中立型时滞项,得到了中立型随机时滞泛函微分方程渐近稳定性的充分判据.在处理各种渐近估计是有效的.     

分数阶中立型微分方程的有限时间稳定(英文)

本文研究了一类分数阶中立型微分方程的有限时间稳定性问题.利用分步法及微分不等式理论,获得了该方程解的存在唯一性及有限时间稳定性结果.推广了文献[8,9]的相关结果.     

On stability of the second order neutral differential equation

There exist a well-developed stability theory for neutral differential equations of the first order and only a few results on functional differential equations of the second order. One of the aims of this paper is to fill this gap. Explicit tests for stability of linear neutral delay differential equations of the second order are obtained.     

具非线性中立项的二阶时滞微分方程的振动性质

By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral delay differential equation of second order.     

Approximation schemes for nonlinear neutral optimal control systems

We discuss methods of approximating stable neutral functional differential equations and associated optimal control problems by sequences of optimal control problems for ordinary differential equations. By introducing a class of “mollified” neutral functional differential equations, convergence of the linear interpolating spline and the averaging approximation scheme is proved. A number of numerical examples are included.     

非线性二阶中立型微分方程的振动性

考虑中立型微分方程我们建立了方程(1)的若干振动准则。这些结果适用于强超线性和强次线性中立型微分方程,且当p(t)≡0时仍然成立。     

Periodic Solutions of Neutral Functional Differential Equations

Periodic neutral functional differential equations are considered.Sufficient conditions for existence, uniqueness and global attractivityof periodic solutions are established by combining the theoryof monotone semiflows generated by neutral functional differentialequations and Krasnosel'skii's fixed-point theorem. These resultsare applied to a concrete neutral functional differential equationthat can model single-species growth, the spread of epidemics,and the dynamics of capital stocks in a periodic environment.     

退化中立型微分系统的常数变易公式和通解

本文讨论退化中立型微分系统，将其分成三组系统，定义两种与其相应的基础解，并分别将其通解求出。从而给出退化中立型微分系统的通解以及常数变易公式，最终得出通解的明确表示，完全推广了常微分方程和时滞微分方程的基本理论。     

Contractivity and exponential stability of solutions to nonlinear neutral functional differential equations in banach spaces

A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained,which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs),neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.