Stability of Neutral Stochastic Differential Equations with Multiple Variable Delays

This paper discusses the pth moment stability of neutral stochastic differential equations with multiple variable delays. The equation has a much more general form than the neutral stochastic differential equations with delay. A new kind of ψ-function is introduced to address the stability, which is more general than the exponential stability and polynomial stability. Using a specific Lyapunov function, a stability criteria for the neutral stochastic differential equations with multiple variable delays is established, by which it is relatively easy to verify the stability of such equations. Finally, the proposed theories are illustrated by two examples.     

Global Solutions and Exponential Stability of Stochastic Functional Differential Equations with Infinite Delay

This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment exponential stability conditions are given. Finally, one example is presented to illustrate our theory.     

马尔可夫调制随机微分方程的平均稳定性

用KRW距离定义马尔可夫调制随机微分方程的稳定性,进而用Markov耦合研究平均稳定性     

Extreme Stability of Functional Differential Equations with Finite Delay

This paper obtained some theorems that can ascertain the zero solution of Junctional differential equations are extremely unitormly stable, extremely asymptotically stable or extremely umlormly asymptotically stable. In the obtained theorems, the derivative of Liapunov function on t along the solutions of Junctional differential equations is not required to be always negative, especially, it may be even positive.     

带脉冲和时滞的二阶微分方程的稳定性

研究了带脉冲和时滞的二阶微分方程的稳定性问题。通过构造合适的Lyapunov函数,利用稳定性理论和脉冲控制方法,证明了对于不稳定的时滞二阶微分方程,可以通过加强一定的脉冲控制使其稳定。获得的结果改进和推广了前人的工作,提供的例子表明了获得结果的有效性。     

两类时滞积分不等式及其应用

本文给出了两类时滞积分不等式,它们是Gronwau不等式以及Bellman-Bihari不等 式的推广。然后以此为工具,讨论了它们在时滞volterro积分方程和高阶泛函微分方 程中的若干应用。