In this paper we show the asymptotic stability of the solutions of some differential equations with delay and subject to impulses. After proving the existence of mild solutions on the half-line, we give a Gronwall–Bellman-type theorem. These results are prodromes of the theorem on the asymptotic stability of the mild solutions to a semilinear differential equation with functional delay and impulses in Banach spaces and of its application to a parametric differential equation driving a population dynamics model.

中文翻译：

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一类分布时滞脉冲微分方程解的渐近稳定性。

在本文中，我们显示了带有时滞并且有脉冲的一些微分方程解的渐近稳定性。在证明半线上存在温和解后，我们给出了Gronwall–Bellman型定理。这些结果是关于Banach空间中具有功能性延迟和脉冲的半线性微分方程的温和解的渐近稳定性的定理的证明，以及它在驱动种群动力学模型的参数微分方程中的应用。