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中文摘要：
讨论了一阶非自治中立型时滞微分方程的广义特征方程及其正解的存在性，利用Picard逼近原理分别得出了该时滞微分方程正解存在的充要条件及广义特征方程的根与正解之间的关系，并给出了该时滞微分方程的解振动的充分条件．
英文摘要：
Generalized characteristic equation and existence of positive solution for a class first-order non-autonomous neutral delay differential equations are investigated. Sufficient and necessary condition of existence of positive solutions are obtained by the mean value theorem and the Picard successive approximation theorem. Meanwhile sufficient conditions of oscillation about the neutral delay differential equations were given.
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