共查询到10条相似文献,搜索用时 312 毫秒
1.
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
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In this paper we consider a linear scalar neutral delay differential equation with variable delays and give some new conditions to ensure that the zero solution is asymptotically stable by means of fixed point theory. These conditions do not require the boundedness of delays, nor do they ask for a fixed sign on the coefficient functions. An asymptotic stability theorem with a necessary and sufficient condition is proved. The results of Burton, Raffoul, and Zhang are improved and generalized.
3.
Guiling Chen Dingshi Li Onno van Gaans Sjoerd Verduyn Lunel 《Indagationes Mathematicae》2018,29(2):671-686
We present new conditions for stability of the zero solution for three distinct classes of scalar nonlinear delay differential equations. Our approach is based on fixed point methods and has the advantage that our conditions neither require boundedness of delays nor fixed sign conditions on the coefficient functions. Our work extends and improves a number of recent stability results for nonlinear functional differential equations in a unified framework. A number of examples are given to illustrate our main results. 相似文献
4.
Ya. B. Zadvorny 《Differential Equations》2018,54(6):716-727
We study the stability and asymptotic stability of the zero solution of autonomous stochastic delay differential equations with discontinuous coefficients by the Lyapunov second method. For the equations under study, we obtain analogs of the Lyapunov stability theorem and the Barbashin–Krasovskii and Zubov asymptotic stability theorems for the zero solution. 相似文献
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In the first part of this paper, we obtain a new property on the module containment for almost periodic functions. Based on it, we establish the module containment of an almost periodic solution for a class of differential equations with piecewise constant delays. In the second part, we investigate the existence, uniqueness and exponential stability of a positive almost periodic and quasi-periodic solution for a certain class of logistic differential equations with a piecewise constant delay. The module containment for the almost periodic solution is established. 相似文献
8.
Yoshiaki Muroya 《Journal of Mathematical Analysis and Applications》2007,326(1):372-389
In this paper, we consider separable nonlinear delay differential systems and we establish conditions for global asymptotic stability of the zero solution. Applying these, we offer improved 3/2-type criteria for global asymptotic stability of nonautonomous Lotka-Volterra systems with delays. 相似文献
9.
Khalil EZZINBI Soumia LALAOUI RHALI 《NoDEA : Nonlinear Differential Equations and Applications》2003,10(1):15-32
The aim of this work is to study the stability for some linear partial functional differential equations. We assume that
the linear part is non-densely defined and satisfies the Hille-Yosida condition. Using the positiveness, we give nessecary
and sufficient conditions independently of the delay to ensure the uniform exponential stability of the solution semigroup.
An application is given for a reaction diffusion equation with several delays.
RID="h1"
ID="h1"This work is supported by the Moroccan Grant PARS MI 36 and TWAS Grant under contract: No. 00-412 RG/MATHS/AF/AC. 相似文献
10.
讨论了一类三阶中立型时滞微分方程的零解的渐近稳定性,借助于构造函数、推广的Halanay一维时滞微分不等式及泰塔格利亚公式,得到了判定其零解是渐近稳定的且与时滞无关的一个充分条件. 相似文献