Some Results Of Normal Families Of Meromorphic Functions

In1925, R.Nevanlinna, Finland mathematician, opened up an important direc-tion in complex analysis, the theory of value distribution, by building the character-istic function and two basic theorems of meromorphic function. As the concept of normal family was introduced in the theory of meromorphic function by P.Montel, the normality of function families has been together with values closely and has become a research branch of the value distribution theory. For several decades, many mathematicians have been attracted to study the normal family. Specially, some Chinese mathematicians, Xiong Qinglai, Yang Lo, Zhang Guanghou, Pang X-uecheng, Sun Daochun, Fang Mingliang, obtained lots of outstanding achievements on the normal family so that the research in China has been in the forefront of normal families in the world. At the end of the last century, the research of normal families has been more active and has become a hot research field in complex analy-sis since W.Schwick studied the normality of meromorphic functions concerning the sharing values. In this paper, we shall study several normal problems of meromor-phic functions related to shared values or shared sets. It consists the following four chapters:First chapter is preliminary knowledge. We introduce some basic knowledge and the classical conclusions of the Nevanlinna theory and the theory of normal family.In the second chapter,we discuss the normal families of meromorphic functions with sharing values.In third chapter,we study the normal families of meromorphic functions which share the sets with the higher derivatives.The fourth chapter is the conclusion. Moreover,we put forward some unsolved and key problems for the thesis.