【作者】 李剑；

【导师】 刘凯；

【作者基本信息】 南昌大学 ， 基础数学， 2020， 硕士

【摘要】 经典的Nevanlinna理论有很多重要的应用,比如研究唯一性问题、研究微分方程亚纯函数解的值分布问题。随着近年来差分Nevanlinna理论的逐步建立,很多差分的唯一性问题和差分方程也相应得到研究。本文主要开展了几类亚纯函数的q-微分差分多项式分担公共值的唯一性问题研究以及一类非线性差分方程的亚纯函数解的研究。论文的结构安排如下:第1章 介绍了本文的研究背景以及主要研究工作;第2章 介绍了一些基本的定义符号,引理及预备知识;第3章 利用公共零点、公共极点的思想,得到了关于几类亚纯函数q-微分差分多项式唯一性的一些结果;第4章 研究了一类非线性差分方程的超级小于1的亚纯解,并得到一些复差分方程及其解的性质;第5章 结论与展望.更多还原

【Abstract】 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.更多还原