Some Research For Normality And Uniqueness Of Meromorphic Functions

Value distribution theory of meromorphic functions,due to R.Nevanlinna in 1925,is one of the most perfect achievements in the last century.It has been well developed in itself and taken big strides to the researches the normal families,the uniqueness of meromorphic functions and complex dynamics etc.This paper involves some results of the author that concern that the normality and the uniqueness of meromorphic functions,under the guidance of supervisor associate professor Chen.The structure of this dissertation are organized as follows.In chapter 1,we describe the value distribution theory of meromorphic func-tions,the normal family theory of meromorphic functions,the uniqueness theory of meromorphic functions and some notations which are used in our paper.In chapter 2,we study the problem of normality of meromorphic functions with multiple values and shared values,and obtain two normality criterions.The results generalize the classic Montel's normality criterion and Bloch-Valiron's normality criterion.Also,examples are given to show that the conditions of the results are necessary.In chapter 3,we continue to investigate the problem of normality of mero-morphic functions with multiple values,and obtain three normality criterions.The results generalize a result of Deng.Moreover,we give some examples to show that some conditions in the Theorems are precise.In chapter 4,we prove a uniqueness theorem of meromorphic functions,which improves a result due to Li-Yi.Meanwhile,we give some examples to demonstrate that the conditions are necessary.In chapter 5,we obtain a uniqueness theorem related to certain meromorphic functions and periodic meromorphic functions,sharing two values,which completely improves the result given by Chen from "1CM+2IM" to "1CM+1IM" in his PhD thesis.Meanwhile,we give some examples to demonstrate that all the conditions are necessary.In chapter 6,we make a summary and present some problems.