中文摘要：

利用Schauder-Tychonoff不动点定理讨论一类三阶拟线性微分方程的振动性理论，分析此方程在满足特殊条件时，其非振动解的结构以及特殊非振动解存在的充分必要条件．

英文摘要：

Using the Schauder-Tychonoff fixed point theorem, the oscillation theory for a class of third- order quasi-linear differential equation was discussed. The structure of its non-oscillatory solutions was an- alyzed for the case when the equation satisfies specific condition and the necessary and the sufficient and necessary conditions for existence of specific no-oscillatory solutions to the equation were given.