OSCILLATION AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF DELAY DIFFERENTIAL EQUATIONS WITH IMPULSES

ＯＳＣＩＬＬＡＴＩＯＮＡＮＤＡＳＹＭＰＴＯＴＩＣＢＥＨＡＶＩＯＲＯＦＳＯＬＵＴＩＯＮＳＯＦＤＥＬＡＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＩＭＰＵＬＳＥＳＳｈｅｎＪｉａｎｈｕａ（申建华）＆ＷａｎｇＺｈｉｃｈｅｎｇ（王志成）（ＨｕｎａｎＵｎ...     

非线性刚性变延迟微分方程单支方法的D-收敛性

This paper is concerned with the error analysis of one-leg methods when applied to nonlinear stiff Delay Differential Equations(DDEs) with a variable delay. It is proved that a one-leg method with Lagrangian linear interpolation procedure is D-convergent of oder p if and only if it is A-stable and consistent of order p in the classical sense for ODEs. The results obtained can be regarded as extension of that for DDEs with constant delay presented by Huang Chenming et al. in 2001     

OSCILLATION OF THIRD ORDER DELAY DIFFERENTIAL EQUATIONS WITH IMPULSES

In this paper we study the oscillation and asymptotic behavior of third order delay differential equations with impulses.Some new sufficient conditions which guarantee that every solution is oscillatory or converges to zero are obtained. Three examples are also given to illustrate our main results.     

ASYMPTOTIC STABILITY FOR GAUSS METHODS FOR NEUTRAL DELAY DIFFERENTIAL EQUATIONS

1. IntroductionIn the past, most of the work on the asymptotic stability for delay and neutra1 delay differential equations dealt with finding the stability region independently of the delay term. AlMutib{l] and recet1y N. Gug1ie1mi [8, 9, 10] reTdsited t…     

N维纯时滞微分方程的稳定性

本文考虑了n维纯时滞微分方程的稳定性,利用分析技巧给出纯时滞微分方程稳定的几个充分条件.当n=1时,所得结论推广和改进了Yorke等人的相应结论.     

SUPERCONVERGENCE OF A DISCONTINUOUS GALERKIN METHOD FOR FIRST-ORDER LINEAR DELAY DIFFERENTIAL EQUATIONS

This paper deals with the discontinuous Galerkin (DG) methods for delay differential equations.By an orthogonal analysis in each element,the superconvergence re...     

二阶脉冲时滞微分方程的振动性

具有固定脉冲时刻的二阶时滞微分方程的解的振动性条件被建立,结果改进和推广了已有文献的相应结果.     

OSCILLATION CRITERIA FOR DELAY DIFFERENTIAL EQUATIONS WITH IMPULSES

The present paper is devoted to the investigation of the oscillation of second order nonlinear delay differential equation (DDE) with impulses, sufficient conditions of oscillation for the solutions of DDE with impulses are obtained by using differential inequality. Some known results are improved and generalized.     

无限滞后测度泛函微分方程的平均化

本文研究了无限滞后测度泛函微分方程的平均化.利用广义常微分方程的平均化方法,在无限滞后测度泛函微分方程可以转化为广义常微分方程的基础上,获得了这类方程的周期和非周期平均化定理,推广了一些相关的结果.     

OSCILLATION FOR A CLASS OF SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH IMPULSES

This paper discusses the oscillation of second-order nonlinear differential equations with impulses.Sufficient conditions for all solutions of the equation to be oscillated are obtained.     

带强迫项的脉冲时滞微分方程的振动性

研究带一阶强迫项的脉冲时滞微分方程的振动性,借助于Kartsatos变换,得到了若干判别这类方程振动的充分性条件,所得的结果推广并改进了时滞微分方程振动性理论中某些已知的相关结果。     

D-CONVERGENCE OF RUNGE-KUTTA METHODS FOR STIFF DELAY DIFFERENTIAL EQUATIONS

1. IntroductionWhen considering the applicability of numerical methods for the solution of the delay differential equation (DDE) y'(t) = f(t, y(t), y(t - T)), it is necessary to analyze the error behaviourof the methods. In fact, many papers have investigated the local and global error behaviour ofDDE solvers (cL[1,2,14]). These error analyses are based on the assumption that the fUnctionf(t,y,z) satisfies Lipschitz conditions in both the last two variables. They are suitable fornonstiff …     

OSCILLATIONS OF SECOND-ORDER HALF-LINEAR DIFFERENTIAL EQUATIONS WITH IMPULSES

A kind of second-order half-linear differential equations with impulses is studied in this paper. Our results improve and generalize some known ones.     

脉冲时滞差分方程的振动性

讨论脉冲时滞差分方程xn+1- xn +pnxn-2 =0 ,n≥ 0 ,n≠ nkxnk+1- xnk =bkxnk,k =1,2 ,3,…给出了方程所有解振动的充分条件     

EXISTENCE RESULTS FOR IMPULSIVE NEUTRAL EVOLUTION DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

This paper is mainly concerned with the existence of mild solutions to a first order impulsive neutral evolution differential equations with state-dependent delay. By suitable fixed point theorems combined with theories of evolution systems,we prove some existence theorems. As an application,an example is also given to illustrate the obtained results.     

《非线性连续分布偏差变元微分方程的线性化振动性》一文的注记

本文主要指出[1]关于时滞微分方程线性化振动的几个定理的错误。     

一阶带参数的时滞微分方程的边值问题

本文利用上下解和单调迭代法，讨论了带参数的一阶时滞微分方程的边值问题，获得了这类问题极值解的存在性定理．     

SPURIOUS NUMERICAL SOLUTIONS OF DELAY DIFFERENTIAL EQUATIONS

This paper deals with the relationship between asymptotic behavior of the numericalsolution and that of the true solution itself for fixed step-sizes. The numerical solution isviewed as a dynamical system in which the step-size acts as a parameter. We present aunified approach to look for bifurcations from the steady solutions into spurious solutionsas step-size varies.     

OSCILLATION RESULTS FOR A SECOND ORDER NEUTRAL DELAY DIFFERENTIAL EQUATIONS

Some new oscillation criteria are established for a second order neutral delay differential equations. These results improve oscillation results of Y.V. Rogo-vchenko for the retarded delay differential equations. The relevance of our theorems is illustrated with two carefully selected examples.     

CONVERGENCE OF PARALLEL DIAGONAL ITERATION OF RUNGE-KUTTA METHODS FOR DELAY DIFFERENTIAL EQUATIONS

Implicit Runge-Kutta method is highly accurate and stable for stiff initial value prob-lem.But the iteration technique used to solve implicit Runge-Kutta method requires lotsof computational efforts.In this paper,we extend the Parallel Diagonal Iterated Runge-Kutta(PDIRK)methods to delay differential equations(DDEs).We give the convergenceregion of PDIRK methods,and analyze the speed of convergence in three parts for theP-stability region of the Runge-Kutta corrector method.Finally,we analysis the speed-upfactor through a numerical experiment.The results show that the PDIRK methods toDDEs are efficient.