具分段常数变元的脉冲微分方程周期解的存在性

通过构造差分方程的周期数列解，研究了一类具有分段常数变元的脉冲微分方程周期解的存在性．     

一类具有逐段常变量微分方程的渐近概周期解

利用差分方程的渐近概周期序列解，讨论了一类具有逐段常变量微分方程的渐近概周期解的存在性．     

带逐段常变量微分方程的伪概周期解

利用伪概周期函数唯一分解性质,研究相关差分方程的伪概周期序列解,并以此为工具得出一类带逐段常变量微分方程伪概周期解的存在唯一性.     

On Quasi-Periodic Solutions of Differential Equations with Piecewise Constant Argument

We study the existence of quasi-periodic solutions to differential equations with piecewise constant argument (EPCA, for short). It is shown that EPCA with periodic perturbations possess a quasi-periodic solution and no periodic solution. The appearance of quasi-periodic rather than periodic solutions is due to the piecewise constant argument. This new phenomenon illustrates a crucial difference between ODE and EPCA. The results are extended to nonlinear equations.     

一类具有逐段常变量微分方程正周期解存在惟一性

利用全连续算子的特征值与α-凹(凸)算子理论,得到了一类具有逐段常变量微分方程正周期解存在性、惟—性及其对参数连续依赖的充分条件．     

Pseudo Almost Periodic Solutions of Nonlinear Hyperbolic Equations with Piecewise Constant Argument

In this paper, we investigate the pseudo almost periodicity of the unique bounded solution for a nonlinear hyperbolic equation with piecewise constant argument. The equation under consideration is a mathematical model for the dynamics of gas absorption,     

带逐段常变量的二阶中立型延迟微分方程的概周期解

本文讨论了带逐段常变量的二阶中立型延迟微分方程(x(t)+px(t-1))″=qx(2[(t+1)/2])+f(t)的概周期解的存在性,此处[.]表示取整函数,p,q是非零实数,|p|=1,q≠-4,f(t)是一个概周期函数.     

带逐段常变量的非线性双曲微分方程的伪概周期解

In this paper,we investigate the pseudo almost periodicity of the unique bounded solution for a nonlinear hyperbolic equation with piecewise constant argument.The equation under consideration is a mathematical model for the dynamics of gas absorption.     

Exponential Stability and Periodic Solutions of Impulsive Neural Network Models with Piecewise Constant Argument

In this paper we introduce an impulsive cellular neural network models with piecewise alternately advanced and retarded argument. The model with the advanced argument is system with strong anticipation. Some sufficient conditions are established for the existence and global exponential stability of a unique periodic solution. The approaches are based on employing Banach’s fixed point theorem and a new integral inequality of Gronwall type with impulses and deviating arguments. The criteria given are easily verifiable, possess many adjustable parameters, and depend on impulses and piecewise constant argument deviations, which provides flexibility for the design and analysis of cellular neural network models. Several numerical examples and simulations are also given to show the feasibility and effectiveness of our results.     

The Existence of Almost Periodic Solutions of Second Order Neutral Differential Equations with Piecewise Constant Argument

51.Intr0ducti0nInthispaper,weconsidertheexistenceofalmostperiodicsoluti0nsforthefoll0wingneutralfunctionaldifferentialebuationwithpiecewiseconstantargument:wherep,qarenonzeroconstants,p(t)lsanalmostper1odicfunctlon,g:RXRXR-Risanalm0stperiodicfunctionintanduniformlyonRXR,andL.jstandsforthegreatest-integerfunction.Notethatforanyintegern,if2n-10)andtheequations(1),(2)areadvanced(orretardedrespectively).Differentialequationswithpiecewiseconstantar…     

逐段常变量微分方程组概周期型解存在唯一性

通过差分方程指数二分法,我们研究了一类具有变系数逐段常变量微分方程组概周期与伪概周期解的存在唯一性与渐近稳定性,改进了已有文献的结果,并且得到了差分方程满足指数二分性的一个充分条件．     

Almost Periodic Solutions of Neutral Differential Difference Equations with Piecewise Constant Arguments

In this paper, we study the existence of almost periodic solutions of neutral differential difference equations with piecewise constant arguments via difference equation methods. Received February 18, 2000, Accepted September 30, 2000.     

Pseudo Almost Periodic Solutions of a Singularly Perturbed Differential Equation with Piecewise Constant Argument

Under suitable assumptions, the existence and the uniqueness of the pseudo-almost periodic solution for a singularly perturbed differential equation with piecewise constant argument are obtained. In addition, the stability properties of these solutions are characterized by the construction of manifolds of initial data.     

A New Almost Periodic Type Solution of First Order Neutral Delay Differential Equations with Piecewise Constant Argument

In this paper, we introduce a new class of ergodic sequences, pseudo almost periodic sequences, and study the existence of pseudo almost periodic sequences to difference equations. On the basis of these, we investigate the existence of pseudo almost periodic solutions for neutral delay differential equations with piecewise constant argument, Received September 21, 1998, Accepted July 6, 1999     

Some Results Concerning a Class of Differential Equations with Piecewise Constant Argument

Under some conditions the asymptotic behavior of the solutions of a class of differential equations with piecewise constant argument is studied.     

带逐段常变量的微分方程的概周期解

本文研究相关差分方程的概周期序列解,并以此为工具得出带逐段常变量的微分方程的概周期解的若干存在性定理．     

Existence of Periodic Solutions in Impulsive Differential Equations

In this paper, we are concerned with the problem of existence of periodic solutions for a class of second order impulsive differential equations. By Poincaré-Bohl theorem, we give several criteria to guarantee that the impulsive differential equation has periodic solutions under assumptions that the nonlinear term satisfies the linear growth conditions. Two specific examples are presented to illustrate the obtained results.     

On Positive Periodic Solutions to Impulsive Differential Equations with Delays

In this paper, by using the Krasnoselskii fixed point theorem on cone compression and expansion, we study the existence of positive periodic solutions of differential equations with impulses and delays, and obtain some new results.     

向前型分段连续微分方程的数值解

本文讨论了向前型分段连续微分方程Euler-Maclaurin方法的收敛性和稳定性,给出了Euler-Maclaurin方法的稳定条件,证明了方法的收敛阶是2n+2,并且得到了数值解稳定区域包含解析解稳定区域的条件,最后给出了一些数值例子用以验证本文结论的正确性.     

具有分段常数变元的时滞微分方程解的振动性(英文)

我们获得了带有分段常数变元的时滞微分方程ｘ′（ｔ）＋ａ（ｔ）ｘ（ｔ）＋∑ｍｉ＝１ｂｉ（ｔ）ｘ（［ｔ－ｉ］）＝０，ｔ≥０所有解振动的新的充分条件，这里［·］定义为最大整数函数．我们的结果改进了文献中的某些已知结果．