泛函微分方程的Lipschitz稳定性

本文给出了泛函微分方程一致Lipschitz稳定的Liapunov－Razumikhin型判据和实例．     

脉冲泛函微分方程的渐近稳定性

讨论了一类脉冲泛函微分方程的渐近稳定性.通过改进 Liapunov泛函的上界,利用Liapunov泛函第二方法和Jensen不等式,得到了一个一致稳定性定理和一个一致渐近稳定性定理,给出的例子说明了所得结果的优越性.     

差分方程解的稳定性、有界性及概周期解的存在性

作者通过Liapunov泛函建立了一类高维差分方程解一致稳定、一致渐近稳定及指数渐近稳定的充要条件. 此外, 作者还证明了解的一致渐近稳定性蕴含解的有界性, 同时也给出了概周期差分方程存在概周期解的一个充分条件.     

中立型泛函微分方程中Liapunov泛函的Razumikhin型定理

本文借助Liapunov泛函附加Razumikhin条件,研究了中立型泛函微分方程解的一致渐近稳定性,统一了Liapunov泛函方法和Razumikhin技巧,所得的结果推广了文[4—8]中的工作。     

具有无限时滞中立型泛函微分方程零解的渐近性态

本文利用 D算子的某些性质及 Liapunov泛函的方法 ,研究了具有无限时滞中立型泛函微分方程零解的一致稳定性与一致渐近稳定性 ,得到了新的结果 .     

具有无限时滞中立型泛函微分方程零解的渐近性态

本文利用D算子的某些性质及Liapunov泛函的方法,研究了具有无限时滞中立型泛函微分方程零解的一致稳定性与一致渐近稳定性,得到了新的结果。     

含无限时滞的混合型偏泛函微分方程初边值问题解的稳定性

本文采用 Liapunov 方法,通过构造向量模与 L_2模混合形式的 Liapunov 泛函,对一类含无限时滞的混合型偏泛函微分方程初边值问题解的稳定性进行了讨论.获得了其平凡解渐近稳定的充分判别条件.     

具连续时滞Liénard方程概周期解的存在唯一性

结合Liapunov泛函，研究了具连续时滞Lienard方程概周期解的存在唯一性和安全一致渐进稳定性。     

脉冲无限时滞微分方程零解的一致渐近稳定性

利用Liapunov泛函和改进的Razumikhin技巧讨论了脉冲无限时滞微分方程零解的一致渐近稳定性,推广和改进了已有文献的结果.     

随机脉冲泛函微分方程的{\boldmath p}阶矩有界性

随机脉冲泛函微分方程是一个具有广泛应用前景的数学模型. 该文利用带Razumikhin条件的Liapunov直接法和比较原理, 得到了随机脉冲泛函微分方程的解的一致(一致且最终、一致且一致最终) p阶矩有界的充分条件, 其中在获得一致有界性和一致最终有界性时, 对dV(t, x(t))/dt 的限制条件也较少, 因此研究结果非常便于应用.     

Stability criteria in terms of two measures for functional differential equations

Results involving uniform stability and uniform asymptotic stability in terms of two measures of delay differential equations by using Liapunov functional techniques are established.     

UNIFORM ASYMPTOTIC STABILITY OF FUNCTIONAL DIFFERENTIAL EQUATIONS

With the help of a Liapunov functional with seml-negative definite derivative,Barbashin-Krasovskii's theorem is extended to nonautonomous functional differentialequations,a reducing dimension approach is presented for the uniform asymptotic stabilityof high dimension systems,and some sufficient conditions of uniform asymptotic stabilityare obtained.     

Stability and boundedness of solutions of neutral functional differential equations with finite delay

Sufficient and necessary criteria are established for the uniform stability and uniformly asymptotic stability of solutions of neutral functional differential equations (NFDEs) with finite delay by using the Liapunov functional approach. We also prove that the uniformly asymptotic stability of solutions implies the existence of bounded solution.     

On liapunov functional in theory of stability of systems with time-lag

It is well known, that in the theory of stability in differential equations, Liapunov's second method may be the most important. The center problem of Liapunov's second method is construction of Liapunov function for concrete problems. Beyond any doubt, construction of Liapunov functions is an art. In the case of functional differential equations, there were also many attempts to establish various kinds of Liapunov type theorems. Recently Burton [2] presented an excellent theorem using the Liapunov functional to solve the asymptotic stability of functional differential equation with bounded delay. However, the construction of such a Liapunov functional is still very hard for concrete problems. In this paper, by utilizing this theorem due to Burton, we construct concrete Liapunov functional for certain and nonlinear delay differential equations and derive new sufficient conditions for asymptotic stability. Those criteria improve the result of literature [1] and they are with simple forms, easily checked and applicable.This project is supported by the National Natural Science Foundation of China.     

Some remarks about stability of nonlinear discrete-time control systems

We study stability and stabilizability properties of nonlinear discrete-time control systems by means of Liapunov functions. We give a characterization of the uniform bounded-input-bounded-state stability property of nonlinear systems in the framework of second Liapunov method. We find an explicit feedback law stabilizing a discrete-time control system affine-in-control under the Jurdjevic-Quinn approach. Received April 2000     

Existence of a global liapunov functional for certain classes of nonlinear distributed systems : PMM vol. 40, n 6, 1976, pp. 1135–1142

The existence of a global Liapunov functional for nonlinear evolutionary equations in a Hilbert space is investigated as a continuation of paper [1], The results obtained represent a generalization of the results of the theory of absolute stability [2, 3], for the systems with infinite dimensional phase space, and are used for investigation of the nonlocal stability and instability of nonlinear distributed systems. The conditions of existence of the global Liapunov functional obtained are illustrated by an example of a nonlinear parabolic system defined in the interval [0, 1], The concept of a Liapunov functional was first introduced and used with success in [4].     

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.     

ON UNIFORM ASYMPTOTIC STABILITY OF INFINITE DELAY DIFFERENCE EQUATIONS

51. IntroductionThe aim of thi8 paPer is to establish the stability criteria for the indnite de1ay differenceequations of the formx(n 1) = F(n,x.) for n E Z, (1'l)where F: Z x CH -- Rk, Z denotes the integer set, Rh is the n-dimensional Euclidean space,CH = {T E C: llWII < H} fOr some constan H > 0, whileC = {yt: {... l --2, --1,0} - Rk l W is bounded}withllytIl = sup IW(8)I for W E C,8<0and x.(8) = x(n 8) for 8 5 0. Here, and in the sequel, l' I is a norm in Rk, and we atwa…     

泛函微分方程的Lipschitz指数稳定性

提出泛函微分方程的Lipschitz指数稳定性概念,给出了利用Liapunov泛函数研究Lipschitz指数稳定性的条件。