中文摘要：

本文研究一类时滞脉冲微分方程解的存在性问题，利用定义上下解对的方法，给出一个新的存在性定理和比较原理．利用该存在性定理和比较原理，作者研究一类具有时滞和脉冲的单种群增长模型，得到这类模型正平衡点的全局吸引性和振动性的新结果．应用方面，考虑具有时滞和脉冲的Hematopoiesis模型，得到了很好的结果．

英文摘要：

In this paper,a definition of a pair of lower-upper solution and a comparision principle for impulsive differential equations with delay are given, while by means of the existence theorem and the comparision principle, some new results about global attractivity and oscillation of solution for a class of models of single species growth are obtained. As exampies,when applieated to some population models, sufficient conditions are provided for global attractivity and oscillation of the equilibrium for this system.