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1)  second order impulsive differential systems
二阶脉冲微分系统
1.
In this paper, the necessary and sufficient conditions of the lower solution and uppersolution are obtained for both the second order impulsive differential systems with periodicboundary value and the first order ones.
文中建立了二阶周期边值脉冲微分系统的上解、下解与一阶周期边值脉冲微分系统的上解、下解的充分必要关系，进一步在维数ｎ≥２时，解决了二阶脉冲微分系统周期边值问题的比较结果。
2)  first order impulsive differential systems
一阶脉冲微分系统
1.
The purpose of this paper is to study the existence and iterative approximation of minimax quasi-solutions for a class of initial value problems of first order impulsive differential systems by using monotone iterative methods.
本文的目的是利用单调迭代方法研究一类一阶脉冲微分系统的初值问题的最小最大拟解的存在性及其迭代逼近程序
3)  impulsive differential system
脉冲微分系统
1.
Bounded Φ-variation solution for a class of impulsive differential systems;
一类脉冲微分系统的Φ-有界变差解
2.
Bounded variation solutions for a class of impulsive differential systems at fixed times
一类固定时刻脉冲微分系统的有界变差解
3.
Stability of a kind of third-order impulsive differential system
一类三阶脉冲微分系统的稳定性
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4)  impulsive differential systems
脉冲微分系统
1.
The practical stability in terms of two measures of impulsive differential systems and its perturbed systems is de-veloped by Lyapunov direct method.
运用李雅普诺夫直接方法研究了脉冲微分系统及其摄动系统关于两个测度的实际稳定性。
2.
By using these theorems, it can conclude stability properties of impulsive differential systems from the corresponding stability properties of the relevant ordinary differential systems.
利用变异 Lyapunov方法 ,讨论了脉冲微分系统依照两种测度的稳定性判定定理 ;在脉冲时刻为固定的情形下 ,得到了关于用常微分系统的稳定性来判定脉冲微分系统稳定性的若干判定定理 ,并改进了已有的多个结果 。
3.
Existence and uniqueness of bounded variation solutions for first order impulsive differential systems at fixed times on a finite interval is discussed and the sufficient conditions of existence and uniqueness of bounded variation solutions for impulsive differential systems are established.
本文借助不连续系统有界变差解理论和脉冲微分系统理论,将文[22]中讨论的一类不连续系统推广到含脉冲情形,并讨论该类固定时刻脉冲微分系统的有界变差解,给出了这类微分系统有界变差解存在性和唯一性定的充分条件。
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5)  second-order impulsive differential equation
二阶脉冲微分方程
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6)  second order differential system
二阶微分系统
1.
We give sufficient conditions for the existence of at least one solution of the second order differential system-x″(t)=f(t,x) with boundary value conditions x(0)=0,x′(1)=0 and x(0)=A,x(1)=B by the method of the lower and upper solutions.
通过推广上下解的概念,利用上下解方法讨论了二阶微分系统-x″(t)=f(t,x)分别在边值条件x(0)=0,x′(1)=0和x(0)=A,x(1)=B下解的存在性。
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补充资料：二阶线性齐次微分方程

二阶线性微分方程的一般形式为

ay"+by'+cy=f(1)

其中系数abc及f是自变量x的函数或是常数。函数f称为函数的自由项。若f≡0，则方程（1）变为

ay"+by'+cy=0（2）

称为二阶线性齐次微分方程，而方程（1）称为二阶线性非齐次微分方程。

说明：补充资料仅用于学习参考，请勿用于其它任何用途。
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