共查询到20条相似文献,搜索用时 15 毫秒
1.
For linear impulsive differential equations, we give a simple criterion for the existence of a nonuniform exponential dichotomy, which includes uniform exponential dichotomies as a very special case. For this we introduce the notion of Lyapunov regularity for a linear impulsive differential equation, in terms of the so-called regularity coefficient. The theory is then used to show that if the Lyapunov exponents are nonzero, then there is a nonuniform exponential behavior, which can be expressed in terms of the Lyapunov exponents of the differential equation and of the regularity coefficient. We also consider the particular case of nonuniform exponential contractions when there are only negative Lyapunov exponents. Having this relation in mind, it is also of interest to provide alternative characterizations of Lyapunov regularity, and particularly to obtain sharp lower and upper bound for the regularity coefficient. In particular, we obtain bounds expressed in terms of the matrices defining the impulsive linear system, and we obtain characterizations in terms of the exponential growth rate of volumes. In addition we establish the persistence of the stability of a linear impulsive differential equation under sufficiently small nonlinear perturbations. 相似文献
2.
Lijun Pan 《Journal of Mathematical Analysis and Applications》2011,382(2):672-685
In this paper, we investigate the pth moment and almost sure exponential stability of impulsive stochastic functional differential equations with finite delay by using Lyapunov method. Several stability theorems of impulsive stochastic functional differential equations with finite delay are derived. These new results are employed to impulsive stochastic equations with bounded time-varying delays and stochastically perturbed equations. Meanwhile, an example and simulations are given to show that impulses play an important role in pth moment and almost sure exponential stability of stochastic functional differential equations with finite delay. 相似文献
3.
考虑了一类带强迫项的脉冲时滞抛物方程组,利用脉冲时滞微分不等式,获得了该类方程组的解强迫振动的若干充分判据. 相似文献
4.
《Applied Mathematics Letters》2007,20(8):839-845
This work studies global exponential stability of impulsive delay differential systems. By employing the Razumikhin technique and Lyapunov functions, several global exponential stability criteria are established for general impulsive delay differential equations. Our results show that delay differential equations may be exponentially stabilized by impulses. An example and its simulation are also given to illustrate our results. 相似文献
5.
脉冲强迫非线性时滞微分方程的渐近性 总被引:3,自引:0,他引:3
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. 相似文献
6.
考虑一类具非线性扩散项的脉冲时滞双曲型偏微分方程的振动性,借助一阶脉冲时滞微分不等式,获得了该类方程在Dirichlet边值条件下所有解振动的若干充分判据. 相似文献
7.
Jurang Yan 《Journal of Mathematical Analysis and Applications》2002,265(2):332-342
The oscillatory and asymptotic behavior of first-order nonlinear delay impulsive differential equations and inequalities is studied. Some new sharp sufficient conditions for oscillation and nonoscillation of solutions of the equations and inequalities are obtained. Many known results are improved. In particular, the conditions are necessary and sufficient if the equations and inequalities are autonomous. 相似文献
8.
非线性脉冲时滞抛物型偏微分方程的强迫振动性 总被引:8,自引:0,他引:8
考虑一类具强迫项的非线性脉冲时滞抛物型偏微分方程,利用脉冲时滞微分不等式,获得了该类方程的解强迫振动的若干充分判据。 相似文献
9.
Yong Duan Peng Tian Shunian Zhang 《Journal of Applied Mathematics and Computing》2003,11(1-2):243-253
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. 相似文献
10.
Oscillatory and Asymptotic Behavior of Solutions for Nonlinear Impulsive Delay Differential Equations 总被引:1,自引:0,他引:1
Wei-hua Mao An-hua Wan 《应用数学学报(英文版)》2006,22(3):387-396
The oscillatory and asymptotic behavior of the solutions for third order nonlinear impulsive delay differential equations are investigated. Some novel criteria for all solutions to be oscillatory or be asymptotic are established, Three illustrative examples are proposed to demonstrate the effectiveness of the conditions. 相似文献
11.
脉冲时滞微分方程解的整体存在唯一性、振动性与非振动性 总被引:28,自引:1,他引:27
本文讨论脉冲时滞微分方程X’(t)=f(t,x(t-T_1(t)),…,x(t-T_n(t))),x(t_k)-x(t_k~-)=I_k(x(t_k~- )).获得了方程(E) 解的一个整体存在唯一性定理.当(E)是线性方程时,给出了由时滞微分方程解的振动性或非振动性刻划出相应的脉冲时滞微分方程的同样性质的一般性脉冲条件. 相似文献
12.
13.
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 相似文献
14.
We construct smooth stable invariant manifolds for a class of delay equations with piecewise constant delay, for any sufficiently small perturbation of a nonuniform exponential dichotomy. We build on former work for perturbations of a uniform exponential dichotomy, also for delay equations with piecewise constant delay. These equations can be described as delay equations with an impulsive behavior of the derivative, such that at certain times the derivative changes abruptly. 相似文献
15.
In this paper, we formulate a robust prey-dependent consumption predator-prey model with a delay of digestion and impulsive perturbation on the prey. Using the discrete dynamical system determined by the stroboscopic map, we obtain a ‘predator-eradication’ periodic solution and show that the ‘predator-eradication’ periodic solution is globally attractive when harvesting for the prey is over certain value. Using a new qualitative analysis method for impulsive and delay differential equations, we prove the system is uniformly persistent when harvesting for the prey is under certain value. Further, we show the delay of digestion is a “profitless” time delay. Moreover, we show our theoretical results by numerical simulation. In this paper, the main feature is that we introduce a delay of digestion and impulsive effects into the predator-prey model and exhibit a new mathematical method which is applied to investigate the system which is governed by both impulsive and delay differential equations. 相似文献
16.
Luis Barreira Claudia Valls 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(5):2542-2563
For nonautonomous linear impulsive differential equations in Banach spaces, we establish the robustness of exponential contractions and exponential dichotomies, in the sense that the exponential behavior persists under sufficiently small linear perturbations. We also consider the more general case of nonuniform exponential behavior. 相似文献
17.
In this paper, by proving a new comparison result, we present a result on the existence of extremal solutions for nonlinear
impulsive delay differential equations. 相似文献
18.
19.
具高阶Laplace算子的非线性脉冲时滞双曲型方程的振动判据 总被引:2,自引:0,他引:2
研究一类具高阶Laplace算子的非线性脉冲时滞双曲型偏微分方程的振动性,利用特征函数法和一阶脉冲时滞微分不等式,获得了该类方程在两类不同边值条件下所有解振动的若干充分性判据.所得结论充分反映了脉冲和时滞在振动中的影响作用. 相似文献
20.
Chunxiang LiJunping Shi Jitao Sun 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(10):3099-3111
This paper is concerned with the stability of n-dimensional stochastic differential delay systems with nonlinear impulsive effects. First, the equivalent relation between the solution of the n-dimensional stochastic differential delay system with nonlinear impulsive effects and that of a corresponding n-dimensional stochastic differential delay system without impulsive effects is established. Then, some stability criteria for the n-dimensional stochastic differential delay systems with nonlinear impulsive effects are obtained. Finally, the stability criteria are applied to uncertain impulsive stochastic neural networks with time-varying delay. The results show that, this convenient and efficient method will provide a new approach to study the stability of impulsive stochastic neural networks. Some examples are also discussed to illustrate the effectiveness of our theoretical results. 相似文献