The Existence Of The Entire Function Solution Of Several Types Of Nonlinear Differential-difference Equations

We study existence of solutions of some nonlinear differential-difference equations,non-linear difference equations and nonlinear differential equations,which lots of experts in complex analysis are interested in.This thesis is structured as follows.In Chapter one,we introduce some background and present situation.In Chapter two,some basic notations and results on Nevanlinna theory and its difference analogues are given.Introduction of exponential polynomials follows.In Chapter three,our work is about existence of solutions of one class of nonlinear differen-tial-difference equation related to expnonential polynomials.Our first result improves Chen,Gao and Zhang's result[Computational Methods and Function Theory,2018,19(1):17-36],which solves Chen,Gao and Zhang's conjecture[Computational Methods and Function The-ory,2018,19(1):17-36]when f(z)is an exponential polynomial.Moreover,we show some examples to illustrate existence of solutions.In Chapter four,we investigate existence of solutions of two classes of nonlinear difference equations.We base the results of Zhang et al[Advances in Difference Equations,2015,2015:150]to consider some equations with similar forms including f~2(z).And we also give some examples.In Chapter five,we study existence of solutions of one class of nonlinear differential e-quation.We improve the result of Chen and Gao[Journal of Computational Analysis and Ap-plications,2018,24(2):137-147]and use the same method to give the partial answers about a question proposed by Li[Journal of Mathematical Analysis and Applications,2011,375:310-319].In the end,the conclusions and prospect of work are given.