退化时滞微分系统的全时滞稳定性

本文利用复Lyapunov方程给出了退化时滞微分系统全时滞渐近稳定的充要条件。     

脉冲差分系统的Robust稳定性

运用Lyapunov函数法分析并建立了脉冲差分系统结构扰动下的R obust稳定性准则.     

脉冲比较微分系统解的φ0-稳定性

本文主要利用分段连续的Lyapunov函数得到脉冲比较微分系统(2)的φ₀-稳定性,并且通过比较方程,得到脉冲微分系统(1)的稳定性.     

分数阶非线性时滞脉冲微分系统的全局Mittag-Leffler稳定性

该文主要研究了含有脉冲和时滞因素的分数阶非线性微分系统的全局Mittag-Lef丑er稳定性.利用分数阶Lyapunov方法和Mittag-Leffler函数性质,给出了含有脉冲时滞分数阶非线性微分系统全局Mittag-Leffler稳定性的充分条件,然后用具体的例子证明了所得结果的有效性.     

变分Lyapunov方法和脉冲时滞微分系统的稳定性

By using the variational Lyapunov method and Razumikhin technique, the stability criteria in terms of two measures for impulsive delay differential systems are established. The known results are generalized and improved. An example is worked out to illustrate the advantages of the theorems.     

脉冲时滞微分系统的弱指数渐近稳定性

研究了脉冲时滞微分系统的弱指数渐近稳定性.利用Razumikhin-Lyapunov函数方法得到系统弱指数渐近稳定的充分判据.提出可脉冲弱指数镇定及脉冲控制模式的概念.对一类较一般的n阶非线性脉冲时滞系统的脉冲镇定问题作了深入探讨.     

非线性有限时滞脉冲泛函微分系统的稳定性

研究了一类非线性有限时滞脉冲泛函微分系统,利用比较原理和Lyapunov函数,得到了系统零解一致最终稳定性及一致最终渐近稳定性的充分条件.     

具分段连续时滞的微分系统的周期解与稳定性

讨论了一类具分段连续时滞的高维微分系统的周期解的存在唯一性和全局渐近稳定性,得到了新的实用的判别条件,推广或改进了文[2-4,6,9]的相关结果..     

时滞差分系统基于两种度量的稳定性分析

本文建立了一些关于时滞差分系统（h0,h）稳定性（一致稳定性，渐近稳定性，一致渐近稳定性）的判定准则。在所得到的定理中，去除了△V为常负的限制，特别地，△V甚至可以恒为正，从而大大改进了已有结果，并更加便于应用。     

时变脉冲时滞微分方程的稳定性

本文讨论脉冲时滞微分方程零解的稳定性 .应用Lyapunov函数法结合Razu mikhin技巧得到这类方程零解一致稳定和渐近稳定的充分性条件 ,并给出例子以说明所得结论     

一类非线性中立型脉冲时滞微分方程解的渐近性

该文研究具有正负系数的非线性中立型脉冲时滞微分方程获得了该方程的每一个解当t→∞时趋于一个常数的充分条件.     

p-Moment Stability of Stochastic Nonlinear Delay Systems with Impulsive Jump and Markovian Switching

Abstract

This article is concerned with the problem of p-moment stability of stochastic differential delay equations with impulsive jump and Markovian switching. In this model, the features of stochastic systems, delay systems, impulsive systems, and Markovian switching are all taken into account, which is scarce in the literature. Based on Lyapunov–Krasovskii functional method and stochastic analysis theory, we obtain new criteria ensuring p-moment stability of trivial solution of a class of impulsive stochastic differential delay equations with Markovian switching.     

Stability Criteria for Solutions of Systems of Linear Deterministic or Stochastic Delay Difference Equations with Continuous Time

We give spectral and algebraic coefficient criteria (necessary and sufficient conditions) as well as sufficient algebraic coefficient conditions for the Lyapunov asymptotic stability of solutions to systems of linear deterministic or stochastic delay difference equations with continuous time under white noise coefficient perturbations for the case in which all delay ratios are rational. For stochastic systems, mean-square asymptotic stability is studied. The Lyapunov function method is used. Our criteria on algebraic coefficients and our sufficient conditions are stated in terms of matrix Lyapunov equations (for deterministic systems) and matrix Sylvester equations (for stochastic systems).     

广义时滞微分方程的渐近稳定性和数值分析

考虑了广义时滞微分方程的初值问题,分析了用线性多步法求解一类广义滞后型微分系统数值解的稳定性,在一定的Lagrange插值条件下,给出并证明了求解广义滞后型微分系统的线性多步法数值稳定的充分必要条件。     

Dynamical Systems Induced by Continuous Time Difference Equations and Long-time Behavior of Solutions

The paper considers the continuous time difference equation x(t + 1) = f(x(t)), t?R ⁺ (?) with f being a continuous interval map. Although the long-time behavior of continuous solutions of Eq. (?) has been extensively described under certain added conditions, there are a number of relatively simple and yet pivotal results for Eq. (?) with no restrictions on f , that were not published. The paper is to compensate for this gap. Herein, properties of the solutions are derived from that of the ω -limit sets of trajectories of the dynamical system induced by Eq. (?) . In particular, if the ω -limit set corresponding a solution x(t) is a cycle or the closure of an almost periodic trajectory, x(t) tends (in the Hausdorff metric for graphs) to a certain upper semicontinuous function.     

Estimates for the L 2-Projection onto Continuous Finite Element Spaces in a Weighted L p -Norm

We consider the orthogonal L₂-projection P onto continuous finite element spaces. We prove estimates for P in a weighted L_p-norm and use these to prove corresponding approximation properties. AMS subject classification (2000) 65N60, 35K85     

两个同类的E_((2))型空间线性等距映射的表现定理

该文得到了两个同类的E_((2))型空间单位球面间等距线性算子的表现定理,这是首次在非具体范数的情形下取得此类结果.     

Asymptotic Behavior of Solutions to a Class of Systems of Delay Differential Equations

The authors investigate the asymptotic behavior of solutions to a class of systems of delay differential equations. It is shown that every bounded solution of such a class of systems tends to a constant vector as t→∞. Our results improve and extend some corresponding ones already known.     

含连续滞量和阻尼项的非线性双曲偏微分方程组的振动性

研究了一类含连续分布滞量和阻尼项的非线性双曲型偏微分方程组运用黎卡提变换获得了该方程组在两类边值条件下解振动的充分条件.