Some Properties Of Solutions Of Differential Difference Equations In Complex Fields

This paper focuses on some differential difference equations and some q-difference differential equations in complex domain.Using Nevanlinna value distribution theory,some value distribution properties of the solutions for these equations are studied.The paper is divided into four chapters,and the content of each chapter is as follows:In the first chapter,we introduce the development and application of the value distribution theory,and explain the background and significance of this research.Next,we introduce the basic content and standard notations about value distribution theory,so as to complete this research better.In the second chapter,we study a type of differential difference equation f(z+1)-f(z-1)+α(z)f’(z)/f(z)=β(z),where α(z),β(z)are non constant rational functions.If f(z)is a finite order transcendental meromorphic solution,some uniqueness results for f(z)and its shift f(z+c)on sharing values are obtained;if f(z)is a finite order transcendental entire solution,we also have the corresponding results.In the third chapter,we study some value distribution properties of the finite order entire solution f(z)for some linear and nonlinear q-difference differential equations.Some examples are given to illustrate the reliability of the results.The fourth chapter is the summary of this paper.We briefly describe the research content and results of this paper again.