两类中立型微分方程正解存在的充分必要条件

Necessary and Sufficient Conditions for the Existence of Nonoscillatory Solutlons to Two Classes of Neutral Equations

本文考虑两类一阶中立型（非）线性微分方程的振动性，得到了其存在非振动解的充分必要条件，从而彻底解决了Chuanxi和Lades[1]中提出的一个公开问题；建立了一系列使振动及非振动的新的充分条件，这些条件推广和改进了已有文献中相应结果．

In this paper, we investigate the oscillations for two classes of first order neutral nonlinear differential equations. The necessary and sufficient conditions for the existence of nonoscillatory solutions of these eguations are obtained, therefore, an open problem which was posted by chuanx and ladax is solved completely. A series of new sufficients for oscillation and nonoscillation of are established, which improve and generalize the known results.