The Propertise Of Meromorphic Solutions Of Some Nonlinear Differential-Difference Equations

In this paper,using Nevanlinna theory and the difference analogue of Nevan-linna theory of meromorphic functions,we investigate the existence,the growth and the distribution of zeros of meromorphic solutions to several kinds of non-linear complex differential-difference equations,and improve and generalize the previous results.It consists of three chapters.In chapter 1,we introduce some basic definitions and properties of meromor-phic functions and entire functions.Some symbols are also introduced.In chapter 2,we investigate the growth and the distribution of zeros of nonlinear differential-difference equations fn(z)+an-1fn-1(z)+…+a1(z)f(z)+q(z)eQ(z)f(k)(z+c)=P(z),where n? 2,k? 1 are integers,q(z),P(z),Q(z)are polynomials,an-1,…,a1 are small functions of f.The relation between the growth and the exponent of convergence of zeros of finite order entire solutions are obtained.In addition,for n=2,the structure of exponential polynomial solutions of the above equations are given.In chapter 3,the existence of meromorphic solutions of nonlinear differential-difference equations fnf'+Qd(z,f)=q(z)eP(z)is investigated,where n? 2 is an integer,Qd(z,f)is a differential-difference polynomial in f of degree d,p(z)is a nonzero entire function,q(z)is a nonzero small function.We obtain the judging conditions on the existence of solutions with hyper-order less than 1.The structure of such solutions are also given.Furthermore,using the obtained result,we investigate the value distribution of a class of nonlinear differential-difference polynomial.