共查询到20条相似文献,搜索用时 156 毫秒
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This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations. 相似文献
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The asymptotic stability of multistep multiderivative methods for systems of delay differential equations 总被引:1,自引:0,他引:1
Chengming HUANG Qianshun CHANG Institute of Applied Mathematics Chinese Academy of Sciences P. O. Box Beijing China 《Communications in Nonlinear Science & Numerical Simulation》2000,5(1)
IntroductionFor many years, many papers investigated the linear stabilit}' of delay differential equation(DDE) solvers and a significant number of important results have already been found for bothRunge-Kutta methods and linear multistep methods (see, for example, [l--8]). In this paper,we firstly consider stability of numerical methods with derivative for DDEs. It is shown thatA-stability of multistep multiderivative methods for ordinary differential equations (ODEs) isequit,alent to p-s… 相似文献
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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
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Gorica Pavlovi? Svetlana Jankovi? 《Journal of Computational and Applied Mathematics》2012,236(7):1679-1690
To the best of the authors’ knowledge, there are no results based on the so-called Razumikhin technique via a general decay stability, for any type of stochastic differential equations. In the present paper, the Razumikhin approach is applied to the study of both pth moment and almost sure stability on a general decay for stochastic functional differential equations with infinite delay. The obtained results are extended to stochastic differential equations with infinite delay and distributed infinite delay. Some comments on how the considered approach could be extended to stochastic functional differential equations with finite delay are also given. An example is presented to illustrate the usefulness of the theory. 相似文献
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Antonín Slavík 《Mathematische Nachrichten》2014,287(11-12):1363-1382
We use the theory of generalized linear ordinary differential equations in Banach spaces to study linear measure functional differential equations with infinite delay. We obtain new results concerning the existence, uniqueness, and continuous dependence of solutions. Even for equations with a finite delay, our results are stronger than the existing ones. Finally, we present an application to functional differential equations with impulses. 相似文献
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Anar T. Assanova Narkesh B. Iskakova Nurgul T. Orumbayeva 《Mathematical Methods in the Applied Sciences》2020,43(2):881-902
A periodic problem for the system of hyperbolic equations with finite time delay is investigated. The investigated problem is reduced to an equivalent problem, consisting the family of periodic problems for a system of ordinary differential equations with finite delay and integral equations using the method of a new functions introduction. Relationship of periodic problem for the system of hyperbolic equations with finite time delay and the family of periodic problems for the system of ordinary differential equations with finite delay is established. Algorithms for finding approximate solutions of the equivalent problem are constructed, and their convergence is proved. Criteria of well-posedness of periodic problem for the system of hyperbolic equations with finite time delay are obtained. 相似文献
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Stability in distribution of stochastic differential equations with Markovian switching and stochastic differential delay equations with Markovian switching have been studied by several authors and this kind of stability is an important property for stochastic systems. There are several papers which study this stability for stochastic differential equations with Markovian switching and stochastic differential delay equations with Markovian switching technically. In our paper, we are concerned with the general neutral stochastic functional differential equations with Markovian switching and we derive the sufficient conditions for stability in distribution. At the end of our paper, one example is established to illustrate the theory of our work. 相似文献
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The main aim of this paper is to study the stability of the stochastic functional differential equations with infinite delay.
We establish several Razumikhin-type theorems on the exponential stability for stochastic functional differential equations
with infinite delay. By applying these results to stochastic differential equations with distributed delay, we obtain some
sufficient conditions for both pth moment and almost surely exponentially stable. Finally, some examples are presented to illustrate our theory. 相似文献
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Stability analysis of highly nonlinear hybrid multiple-delay stochastic differential equations 下载免费PDF全文
Chen Fei Weiyin Fei Xuerong Mao Mingxuan Shen Litan Yan 《Journal of Applied Analysis & Computation》2019,9(3):1053-1070
Stability criteria for stochastic differential delay equations (SDDEs) have been studied intensively for the past few decades. However, most of these criteria can only be applied to delay equations where their coefficients are either linear or nonlinear but bounded by linear functions. Recently, the stability of highly nonlinear hybrid stochastic differential equations with a single delay is investigated in [Fei, Hu, Mao and Shen, Automatica, 2017], whose work, in this paper, is extended to highly nonlinear hybrid stochastic differential equations with variable multiple delays. In other words, this paper establishes the stability criteria of highly nonlinear hybrid variable multiple-delay stochastic differential equations. We also discuss an example to illustrate our results. 相似文献
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本文讨论了线性时滞微分方程的点态退化问题.借助于矩阵的有关知识,我们给出了判定n阶时滞微分方程点态退化的充分必要条件及代数判据. 相似文献
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Under mild conditions a delay semigroup can be transformed into a (generalized) contraction semigroup by modifying the inner product on the (Hilbert) state space into an equivalent inner product. Applications to stability of differential equations with delay and stochastic differential equations with delay are given as examples. 相似文献
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The authors discuss one type of general forward-backward stochastic differential
equations (FBSDEs) with It?o’s stochastic delayed equations as the forward equations and
anticipated backward stochastic differential equations as the backward equations. The
existence and uniqueness results of the general FBSDEs are obtained. In the framework
of the general FBSDEs in this paper, the explicit form of the optimal control for linearquadratic
stochastic optimal control problem with delay and the Nash equilibrium point
for nonzero sum differential games problem with delay are obtained. 相似文献
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Kazuyuki Matsui Hideaki Matsunaga Satoru Murakami 《Nonlinear Analysis: Theory, Methods & Applications》2008
For functional differential equations in a Banach space, we obtain some results on the asymptotic behavior of solutions, which correspond to Perron type theorems for differential equations without delay or with finite delay. 相似文献
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The stability and boundedness of the solution for stochastic functional differential equation with finite delay have been studied by several authors, but there is almost no work on the stability of the solutions for stochastic functional differential equations with infinite delay. The main aim of this paper is to close this gap. We establish criteria of pth moment ψγ(t)-bounded for neutral stochastic functional differential equations with infinite delay and exponentially stable criteria for stochastic functional differential equations with infinite delay, and we also illustrate the result with an example. 相似文献
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Differential algebraic equations with after-effect 总被引:4,自引:0,他引:4
C. T. H. Baker C. A. H. Paul H. Tian 《Journal of Computational and Applied Mathematics》2002,140(1-2):63-80
In this paper, we are concerned with the solution of delay differential algebraic equations. These are differential algebraic equations with after-effect, or constrained delay differential equations. The general semi-explicit form of the problem consists of a set of delay differential equations combined with a set of constraints that may involve retarded arguments. Even simply stated problems of this type can give rise to difficult analytical and numerical problems. The more tractable examples can be shown to be equivalent to systems of delay or neutral delay differential equations. Our purpose is to highlight some of the complexities and obstacles that can arise when solving these problems, and to indicate problems that require further research. 相似文献
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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
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《Mathematische Nachrichten》2018,291(13):2045-2056
We study the existence and uniqueness of solutions, and the wellposedness of a general class of second order abstract differential equations with state‐dependent delay. Some examples related to partial differential equations with state‐dependent delay are presented. 相似文献
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Ravi P. Agarwal Alexander Domoshnitsky Abraham Maghakyan 《Czechoslovak Mathematical Journal》2015,65(4):1047-1068
We propose a new method for studying stability of second order delay differential equations. Results we obtained are of the form: the exponential stability of ordinary differential equation implies the exponential stability of the corresponding delay differential equation if the delays are small enough. We estimate this smallness through the coefficients of this delay equation. Examples demonstrate that our tests of the exponential stability are essentially better than the known ones. This method works not only for autonomous equations but also for equations with variable coefficients and delays. 相似文献