一类具有脉冲的向量型时滞微分系统的振动性

The Oscillations of A Class of Delay Differential System with Impulse

研究了一类向量型时滞脉冲微分方程系统的振动性问题,通过作变最变换,将常系数脉冲微分方程系统变为变系数非脉冲微分方程系统,得到了模型非振动解的渐近性态和方程任意解振动的充分条件,利用留数理论,得到了方程广义振动和广义非振动的充分条件。

A non-linear systems of differential equation with impulse is considered. By taking transform, the uncontinuous impulsive differential equation with constant coefficients is transformed to continuous un-impulsive differential equation with changable coefficients. The sufficient condition for the oscillatory of every solution and the asymptotic behavior of the nonoscillatory solution are obtained. By using Laplace-transform and residue theory, the sufficient conditions for the generic oscillation and nonoscillation of the system are obtained.