第二类Abel方程的反射函数及其周期解

Reflective function and periodic solution of the second class of Abel equation

研究第二类Abel方程以某函数为反射函数的简单微分方程时该反射函数的结构形式,讨论了该Abel方程以这种形式的函数为反射函数的充分条件,并应用所得结果探讨了第二类Abel方程以及与其等价的微分方程类的周期解的几何性状.

This article discusses the structure of the reflective function of the second class of Abel equation when it is a simple differential equation.Under this condition the sufficient conditions for the existence of the above-mentioned reflective function of the second class of Abel equation are established.The results are applied to discuss the geometric property of the periodic solutions of the second class of Abel equation.