Researches On Value Distribution Of Meromorphic Functions Of Difference Equations And Difference Operators

In the 1920s,since the Finnish mathematician Rolf Nevanlinna established the theory system of meromorphic function value distribution,Nevanlinna value distribution theory has always been an important branch of complex analysis.In recent years,the theory of meromorphic function value distribution has been continuously improved,also provides new methods and ideas for complex difference and difference equations.This paper we firstly discuss the uniqueness problem of the meromorphic solutions of a class of -difference equations shared values with a meromorphic function.Secondly,the properties of the difference operators and the meromorphic function with shared value are characterized.The main structure of the dissertation is as follows:Chapter 1 is preliminary knowledge.We briefly introduce the basic Nevanlinna theory with the common notations and the main results of the uniqueness theory of meromorphic functions and the theory of complex domain difference analogues of value distribution.In the second chapter,we first investigate the meromorphic solution of a class of homogeneous second-order -difference equations and the uniqueness problem of a meromorphic function with three shared values.The obtained results generalizes the results of Yang Yin and Ye Yasheng.Then we have discussed the uniqueness problem of the meromorphic solution of a class of nonhomogeneous -difference equations and a meromorphic function shared four values.In the third chapter,we mainly research the meromorphic function properties of transcendence and value distribution when meromorphic functions shared values with its difference operators.Furthermore,the expressions of the function is characterized.Chapter 4 is the summarizes and prospects.We sum the contents of this thesis and list some problems to be solved.