摘要
In this paper we will investigate the multiplicity of zero solution for a class of Abel equation, and obtain better estimation on multiplicity than that given by Alwash and Lloyd for the equation of a certain form, and solve a conjecture posed by Ye Yanqian for the equation of another form. As a by-product, the considered equation may have at least four small amplitude limit cycles. The method of this paper is useful for computing the focal value of a critical point of focus type for polynomial system that can be transformed into Abel equation or Abel form.
In this paper we will investigate the multiplicity of zero solution for a class of Abel equation, and obtain better estimation on multiplicity than that given by Alwash and Lloyd for the equation of a certain form, and solve a conjecture posed by Ye Yanqian for the equation of another form. As a by-product, the considered equation may have at least four small amplitude limit cycles. The method of this paper is useful for computing the focal value of a critical point of focus type for polynomial system that can be transformed into Abel equation or Abel form.
基金
This research is supported by the National Natural Science Foundation of China(No.19901013).
