共查询到20条相似文献,搜索用时 390 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
2.
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
11.
1 IntroductionConsider the following functional differential equationX'(t) = A(t)x(t) [' C(t,s)x(s)ds, (1)icwhere x E m; A(t) = (ail(t))... is a n x n function matrix, which continuesin [0, co); C(t,s) = (qj(t,8))... is a n x n function matrix, which conti-nues when 0 5 s 5 t < co, and L oo IIC(u,t)lldu continues in [0, co).The problem on the stability for the zero solution of (1) has been studied bymany papers. But in the known results, the boundedness of j: IIC(t, s)lldsor L " IIC… 相似文献
12.
Julio G. Dix Ioannis K. Purnaras 《Journal of Mathematical Analysis and Applications》2006,318(1):296-304
In this article we study asymptotic properties of solutions to first order linear neutral differential equations with variable coefficients and constant delays. Results are stated in terms of the solution to a characteristic equation. By doing this, we extend some of the results obtained for delay equations in [J.G. Dix, Ch.G. Philos, I.K. Purnaras, An asymptotic property of solutions to linear non-autonomous delay differential equations, Electron. J. Differential Equations 2005 (2005) 1-9] to neutral equations. 相似文献
13.
This paper considers the asymptotic stability analysis of both exact and numerical solutions of the following neutral delay differential equation with pantograph delay.where $B,C,D\in C^{d\times d},q\in (0,1)$,and $B$ is regular. After transforming the above equation to non-automatic neutral equation with constant delay, we determine sufficient conditions for the asymptotic stability of the zero solution. Furthermore, we focus on the asymptotic stability behavior of Runge-Kutta method with variable stepsize. It is proved that a L-stable Runge-Kutta method can preserve the above-mentioned stability properties. 相似文献
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By constructing some suitable Lyapunov-type functionals and applying the theory of the definite-quadratic form, we obtain the stability of the zero solution of two classes of evolution equations with delays, including reaction–diffusion equations and damped wave equations. Our criteria depend on the derivatives of delays. Consequently, when the delays are constants, these criteria are independent of the magnitudes of the delays, so the delays are harmless for the stability of the zero solution. 相似文献
15.
Jiaowan Luo 《Journal of Mathematical Analysis and Applications》2007,334(1):431-440
In this paper we consider a linear scalar neutral stochastic differential equation with variable delays and give conditions to ensure that the zero solution is asymptotically mean square 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 mean square stability theorem with a necessary and sufficient condition is proved. Some well-known results are improved and generalized. 相似文献
16.
《Journal of Computational and Applied Mathematics》2005,174(2):201-211
In this paper, we study stability of periodic solutions of a class of nonlinear functional differential equations (FDEs) with state-dependent delays using the method of linearization. We show that a periodic solution of the nonlinear FDE is exponentially stable, if the zero solution of an associated linear periodic linear homogeneous FDE is exponentially stable. 相似文献
17.
Dingheng Pi 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(2):639-651
In this paper, we study the stability properties of solutions of a class of functional differential equations with variable delay. By using the fixed point theory under an exponentially weighted metric, we obtain some interesting sufficient conditions ensuring that the zero solution of the equations is stable and asymptotically stable. 相似文献
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In this paper, we investigate stochastic asymptotic stability of the zero solution for certain third-order nonlinear stochastic delay differential equations by constructing Lyapunov functionals. 相似文献
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Inmathematicalbiology,therehavebeenmanybio1ogicalmodelsinpopu-1ationdynamcis,ecologyandepidemic,whicharedescribedbyautonomousdelaydifferentialequations.Theasymptoticstabilityofthosen1ode1sisinte-resting,whichhavebeenstudiedbymanyauthors[1-4].Thepurposeoft… 相似文献