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Oscillation criteria for a first-order impulsive neutral differential equation of Euler form

机译:欧拉形式的一阶脉冲中立型微分方程的振动准则

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In this paper, we are concerned with the oscillation of a first-order impulsive neutral differential equation of Euler form with variable delays. Our results reveal the fact that the oscillatory behavior of all solutions of differential equations without impulses can be inherited by impulsive differential equations under certain impulsive perturbations. It is also seen that the oscillatory properties of all solutions of impulsive differential equations may be caused by the impulsive perturbations, though the corresponding differential equations without impulses admit a nonoscillatory solution. Some examples are also given to illustrate the applicability of the results obtained.
机译:在本文中,我们关注一类具有可变时滞的欧拉形式的一阶脉冲中立微分方程的振动性。我们的结果揭示了一个事实,即在一定的脉冲扰动下,所有不带脉冲的微分方程解的振动性都可以由脉冲微分方程继承。还可以看到,脉冲微分方程所有解的振动性质可能是由脉冲微扰引起的,尽管没有脉冲的相应微分方程也具有非振荡解。还提供了一些示例以说明所获得结果的适用性。

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