【作者】 刘红；

【导师】 高凌云；

【作者基本信息】 暨南大学 ， 基础数学， 2012， 硕士

【摘要】 本文利用亚纯函数的Nevanlinna值分布理论以及借助复微分方程的研究技巧，分别研究了代数微分方程组允许解的存在性问题，q-差分多项式的值分布以及q-差分方程解的存在性问题，推广了以前一些文献的结果。全文共分四个部分：第一部分，主要介绍Nevanlinna值分布理论的基础知识,常用记号和一些基本定理以及与复q-差分有关的一些基本定理。第二部分，对一类复高阶微分方程组的允许解进行了讨论,将以前一些文献中的关于方程组允许解的结论进行推广,得到了类似的结论。第三部分，对一类复q-差分多项式的零点问题进行研究，得到了与复差分类似的结果。第四部分，讨论了一类复q-差分方程的解存在性问题，得到了几个结果。更多还原

【Abstract】 In this paper, using the Nevanlinna theory of the distribution of meromophicfunctions and the investigation skills of complex differential equations, we investigatethe problem of the existense of admissible solutions of a type of algebraic equations,the value distribution of q-difference polynomials and the meromorphic solutions ofcertain q-difference equations. Some results are improved and generalized. This thesisis divided into four parts:The first part mainly introduced the foundation knowledge of Nevanlinna valuedistribution theory including usual notation, definitions and fundamental theorem.Also, we introduced some fundamental theorem of the q-difference.The second part, the existense of admissible solutions of a type of algebraicequations of a class of complex high order differential equations is discussed, Someresults are improved and generalized, obtained the similar results.The third part discussed the zero point of a class of complex q-differentialpolynomial, obtained the similar results with difference polynomials.The fourth part discussed the solutions of a class of complex q-differenceequation, obtained some results.更多还原