| The classical Nevanlinna theory has many important applications,such as the study of uniqueness problems,the study of the value distribution problem on meromorphic solutions of differential equations.With the establishment of the difference Nevanlinna theory in recent years,many difference unique problems and difference equations have been studied.In this thesis,we mainly investigates the uniqueness problems on the q-differential difference polynomials of meromorphic functions and the meromorphic solutions on non-linear difference equations of certain type.We arrange this paper as follows.In chapter 1,we introduce the background and the main research 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,using the idea of common zeros and common poles,some results are obtained about the uniqueness on several types of q-differential differential polynomials of meromorphic functions.In chapter 4,we investigate the meromorphic solutions with hyper-order less than one on non-linear difference equations of certain types,and some properties on these solutions are obtained.In chapter 5,we give the expectations based on our results. |
