Some Researches On Distribution Theory Of Meromorphic Functions

In 1920s,Rolf Nevanlinna introduced the characteristic functions of meromor-phic functions and established the famous Nevanlinna theory.Nearly half a century,the uniqueness theory of meromorphic functions has a gradually development to be an important branch of complex analysis.At present,the value distribution theory of meromorphic functions is still an international frontier research direction,espe-cially the uniqueness theory of meromorphic functions and the theory of complex differential equations.In this thesis,we will study the meromorphic solutions of a class of nonlinear complex differential equations and periodicity and shared value of meromorphic functions.The thesis is structured as follows.Section one is preliminary knowledge.We present the basic Nevanlinna theory and some classical theories of the uniqueness results.In section two,we mainly discuss a class of nonlinear complex differential e-quations.We will introduce some previous results on complex differential equations involving exponential functions by Chung-Chun Yang,Ping Li,Liang.wen Liao,etc.Then we study the meromorphic solutions of a class of nonlinear complex differential equations involving exponential functions.The results extend Theorem 1 in Jianjun Zhang,Xinping Xu,Liangwen Liao[Meromorphic solutions of nonlinear complex differential equations(in Chinese).Sci Sin Math,2017,47:1-14].Moreover,we show by a example that our results are precise in certain senses.In section three,we mainly discuss the periodicity and shared value of meromor-phic functions.Then we use Nevanlinna theory to discuss the period of meromorphic functions and obtain an interesting result.Moreover,some examples are given to illustrate that the conditions are necessary.In section four,the summary and some problems are presented.