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1.
This paper considers the stability problem for a class of impulsive systems of functional differential equations. By using Lyapunov functions and the Razumikhin technique, several stability criteria in terms of two measures are established. Some examples are worked out to illustrate the theorems. 相似文献
2.
This paper establishes several stability criteria for perturbed impulsive integro-differential equations with fixed moments of impulsive effect. By using a new comparison theorem, which connects the solutions of perturbed system and the unperturbed one, some sufficient conditions for the stability in terms of two measures are obtained for the perturbed system while unperturbed one dissatisfied which because of the effect of the perturbed terms. 相似文献
3.
In this work, we consider a new approach to the practical stability theory of impulsive functional differential equations. With Lyapunov functionals and Razumikhin technique, we use a new technique in the division of Lyapunov functions, given by Shunian Zhang, and obtain conditions sufficient for the uniform practical (asymptotical) stability of impulsive delay differential equations. An example is also discussed to illustrate the advantage of the proposed results. 相似文献
4.
5.
In this paper, we study the stability of nonlinear impulsive stochastic differential equations in terms of two measures. The concept of perturbing Lyapunov functions is introduced to discuss stability properties of solutions of nonlinear impulsive stochastic differential equations in terms of two measures. By using perturbing Lyapunov functions and comparison method, some sufficient conditions for the above stability are given. 相似文献
6.
《Journal of Computational and Applied Mathematics》2005,176(1):223-229
In this paper we introduce a new stability—eventual practical stability for impulsive differential equations with time delay. By using Lyapunov functions and comparison principle, we will get some criteria of eventual practical stability, eventual practical quasistability and strong eventual practical stability for impulsive differential equations with time delay in terms of two measurements. 相似文献
7.
Practical stability of impulsive hybrid differential systems in terms of two measures on time scales
In this paper, we establish a new comparison theorem on time scales, and give some new stability criteria for impulsive hybrid differential systems. 相似文献
8.
9.
10.
11.
Bashir Ahmad 《Applied mathematics and computation》2009,214(1):83-89
In this paper, we study the stability criteria in terms of two measures for perturbed delay integro-differential equations with fixed moments of impulsive effect by using variational Lyapunov method together with a comparison principle. 相似文献
12.
We consider the asymptotic stability problems by Lyapunov functionals V for a class of functional differential equations with impulses of the form x′(t)=f(t,x
t
), x∈R
n
, t≧t
0, t≠t
k
; △x=I
k
(t,x(t
−)), t=t
k
, k∈Z
+
. Some new asymptotic stability results are presented by using an idea originated by Burton and Makay [6] and developed by
Zhang [1]. We generalize some known results about impulsive functional differential equations in the literature in which we
only require the derivative of V to be negative definite on a sequence of intervals I
n
=[s
n
,ξ
n
] which may or may not be contained in the sequence of impulsive time intervals [t
n
,t
n+1). 相似文献
13.
M.U. Akhmet 《Journal of Mathematical Analysis and Applications》2003,288(1):182-196
Criteria for stability, asymptotical stability and instability of the nontrivial solutions of the impulsive system
14.
Eduardo Hernández 《Mathematical and Computer Modelling》2011,53(1-2):196-204
We study the existence of mild solutions for a class of impulsive neutral functional differential equation defined on the whole real axis. Some concrete applications to ordinary and partial neutral differential equations with impulses are considered. 相似文献
15.
Gani Tr. Stamov 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(5):2457-2464
This paper studies the existence and uniqueness of exponentially stable almost periodic solutions for abstract impulsive differential equations in Banach space. The investigations are carried out by means of the fractional powers of operators. We construct an example to illustrate the feasibility of our results. 相似文献
16.
《Applied Mathematics Letters》2005,18(6):701-706
Results involving uniform stability and uniform asymptotic stability in terms of two measures of delay differential equations by using Liapunov functional techniques are established. 相似文献
17.
We obtain sufficient conditions for the stability of solutions of nonlinear systems of impulsive differential equations in a cone. The main tool in our study is the comparison principle suggested in the paper. This approach permits one to study critical cases; it is illustrated by examples of nonlinear systems for which the trivial orbit of the continuous and discrete components is simultaneously unstable. 相似文献
18.
Xiaodi Li T. Caraballo R. Rakkiyappan Xiuping Han 《Mathematical Methods in the Applied Sciences》2015,38(14):3130-3140
In this paper, the stability problem of impulsive functional differential equations with infinite delays is considered. By using Lyapunov functions and the Razumikhin technique, some new theorems on the uniform stability and uniform asymptotic stability are obtained. The obtained results are milder and more general than several recent works. Two examples are given to demonstrate the advantages of the results. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
19.
Yu Zhang 《Journal of Mathematical Analysis and Applications》2005,301(1):237-248
Strict stability is the kind of stability that can give us some information about the rate of decay of the solutions. There are some results about strict stability of differential equations. In the present paper, we shall extend the strict stability to impulsive functional differential equations. By using Lyapunov functions and Razumikhin technique, we shall get some criteria for the strict stability of impulsive functional differential equations, and we can see that impulses do contribute to the system's strict stability behavior. 相似文献
20.
A. L. Zuev 《Ukrainian Mathematical Journal》2006,58(5):709-717
We consider the problem of partial asymptotic stability with respect to a continuous functional for a class of abstract dynamical
processes with multivalued solutions on a metric space. This class of processes includes finite-and infinite-dimensional dynamical
systems, differential inclusions, and delay equations. We prove a generalization of the Barbashin-Krasovskii theorem and the
LaSalle invariance principle under the conditions of the existence of a continuous Lyapunov functional. In the case of the
existence of a differentiable Lyapunov functional, we obtain sufficient conditions for the partial stability of continuous
semigroups in a Banach space.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 5, pp. 629–637, May, 2006. 相似文献