THE MULTIPLICITY OF ZERO AND LIMIT CYCLES FOR ABEL EQUATIONS

作     者：ZHANG Xiang (Department of Mathematics, Nanjing Normal University, Nanjing 210097, China) ZHANG Xiang (Department of Mathematics, Nanjing Normal University, Nanjing 210097, China)

作者机构：南京师范大学 江苏 南京 210097 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2001年第14卷第2期

页      面：165-173页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：This research is supported by the National Natural Science Foundation of China(No.19901013) 

主　　题：Abel equation multiplicity limit cycle. 

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.