Studies On The Periodicity Of Differential Difference Polynomials And Entire Solutions Of Functional Differential Equation

The value distribution theory created by the Finnish mathematician R.Nevanlinna is one of the important methods for studying complex analysis problems,for example,considering the uniqueness of meromorphic functions,the value distribution of meromorphic function solutions of differential equations,etc.With the establishment of the difference version of the Nevanlinna value distribution theory,many differential equations and periodicity problems related to differences have been studied.This dissertation studies the periodicity of entire functions from Yang's conjecture and a certain type functional differential equation combining the methods of Zhang and Yi [27]In chapter 1,we briefly introduce the research background and main work of this paper.In chapter 2,we introduce some symbols,definitions and lemmas that will be used in the proof of result in this paper.In chapter 3,we introduce the generalized Yang's conjecture and its related results,then study the periodicity of entire functions and their differential polynomials.In chapter 4,we mainly consider the periodicity of entire functions and their differential-difference polynomials.In chapter 5,we mainly study a certain type functional differential equation f(z1+ z2)= f(z1)f(z2)-f(z1)f(z2),and some results of solutions are obtained.In chapter 6,we obtain the expectations based on our results.