Assume that . in this paper , we will discuss the existence , the non - existence and the uniqueness of limit cycle system ( * ) . the methods employed are poincare - bendixsion theorem , method of dulac function and zhang zhifen ' s uniqueness theorem . our main results are as follows : theorem 1 对的情形,我们讨论了系统（ * ）极限环的存在性、不存在性和唯一性。主要利用环域定理、 dulac函数法和张芷芬的唯一性定理等手法。
In the third chapter , we derive a new family of deformed halley methods without the evaluation of the second frechet - derivative to approximate the roots of nondifferentiable equations in banach space . we also provided a existence - uniqueness theorem and a new system of recurrence relations 在第三章中，构造了一族避免二阶fre chet导数的修正halley迭代，用其去逼近banach空间中非线性算子方程的解，同时给出了存在唯一性定理和一种新型的递归关系。
This thesis study the uniqueness theory of meromorphic functions . with the theory of nevanlinna ' s value distribution , the author analyze and study the unique problems about meromorphic function and its derivative or differential polynomial shared values , two meromorphic functions shared one value , the derivatives of meromorphic functions shared one value or small function , the derivatives of meromorphic functions shared one set . proved several uniqueness theorem , which generalized and improved the results of qiu gandi , brosch , yi hongxun , c . c . yang and wu guirong , 作者应用nevanlinna值分布理论，对函数与其导函数或微分多项式具有公共值，两函数具有公共值，两函数的导函数分担公共值或小函数，以及分担公共值集的唯一性等问题进行了分析和研究，得到了几个唯一性定理，它们分别是邱? ? ， brosch ，仪洪勋，杨重骏，吴桂荣等人的有关结果的推广和改进。
This thesis studies the uniqueness theory of meromorphic functions . firstly , the author proved three sharing sets " uniqueness theorems which improved the results of yi hongxun , li jiangtao . then , the thesis improved the results of qiu gandi about meromorphic function and its derivative sharing values . finally , we obtain the exact hayman inequality and its application 本论文主要研究的是亚纯函数的唯一性理论。首先,作者应用值分布理论，证明了三个有关集合分担的唯一性定理，它推广了仪洪勋，李江涛等人的结果。
