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

Using Nevanlinna theory and corresponding difference analogue theory,this thesis investigates the solutions on a type of non-linear differential-difference equations.More specially,we investigate the existence and growth of the solutions,the relationship between growth order and exponents of convergence,etc.In addition,we also study the value distribution of a type of non-linear differential-difference polynomials.We arrange this paper as follows.In chapter 1,we introduce the research background ofthe non-linear differential-difference equations and polynomials,and the main work of this paper.In chapter 2,we introduce some definitions,symbols and lemmas which are necessary in the proof of our results.In chapter 3,we investigate the conditions on the existence,the relationship between the growth order and the exponents of convergence of zero on the solutions and the relationship between numerator and denomination of rational solutions on a type of non-linear differential-difference equation related to the Painleve difference equations.In chapter 4,we investigate the value distribution of a type of non-linear differential-difference polynomials related to the Hayman’s conjecture.In chapter 5,we give the expectations based on our results.