Studies On Exponential Polynomial Solutions Of Non-linear Complex Differential-Difference Equations And The Value Distribution Of Complex Differential-Difference Polynomials

The properties of exponential polynomial solutions for differential-difference equations and the value distribution for several kinds of differential-difference polynomials and difference polynomials are studied by using the Nevanlinna theory and its difference simulation theory in complex analysis as the main tool in this paper.The content of the paper is arranged as follows:Chapter 1 introduces some basic concepts in Nevanlinna theory and some lemmas needed in this paper.In chapter 2,the exponential polynomial solutions of a class of nonlinear differential-difference equations and the meromorphic solutions of a class of linear differential-difference equations are studied.In chapter 3,we investigate the zero distribution of several kinds of exponential polynomial differential polynomials and differential differential polynomials.In chapter 4,the zero distribution of some kinds of differential polynomials and differential-difference polynomial is studied.The conclusion and prospect are of the 5th chapter.