Some Research On The Problem Of Closed Solution Of Abel Equation

This paper includes four chapters.The first chapter is overview, in which we introduce the closed solution and center of Abel equation, some relative important results and the authors' work.In the second chapter, the existence, uniqueness and only-two property of Abel equation's limit cycles are discussed, and the relative results of Wang Rongliang and Wu Changzhi, Zhang Jianfeng are improved.In the third chapter, making use of the results about Abel equation, we discuss the existence, number and stability of the limit cycles of polynomial systems. The relative work of Shui Shuliang and Cai Suilin is generalized.In the fourth chapter, some general equations are studied, of which Abel equation and some equations that have been intensively studied are the special cases. We obtain the theorems about the upper bound and existence of closed solution under some conditions, which generalize and improve the relative work of A.Gasull and J.Llibre, Wang Rongliang and Wu Changzhi, Feng Zhaosheng, Zhang Peijun and Zhang Houyang, Feng Zhaosheng and Fei Shumin.