全纯曲线的第二基本定理的差分模拟以及费马型微分差分方程解的性质
发布时间：2019-03-09 13:27
【摘要】：第二基本定理在Nevanlinna值分布理论中占有很重要的地位,可以用它来解决复微分方程和差分方程中很多问题,甚至直接可以判断方程的解是否存在和唯一性。故Nevanlinna理论的第二基本定理形式是非常重要。本学位论文内容包括:第1章介绍本学位论文的研究背景和主要的工作;第2章介绍Nevanlinna理论中的基础知识和本文中用到的相关知识;第3章介绍运用高等代数中的线性方程和矩阵的知识将单复变量到复射影空间中分担超平面的差分形式下的第二基本定理的结果成功地推广到单复变量到复射影空间中分担超曲面的差分形式下的第二基本定理及其相关的结论;第4章介绍费马型微分差分方程解的值分布的一些结果。
[Abstract]:The second fundamental theorem plays an important role in Nevanlinna's value distribution theory. It can be used to solve many problems in complex differential equation and difference equation, and even to judge the existence and uniqueness of the solution of the equation directly. Therefore, the form of the second fundamental theorem of Nevanlinna's theory is very important. The contents of this dissertation include: chapter 1 introduces the research background and main work of this thesis; the second chapter introduces the basic knowledge of Nevanlinna theory and the related knowledge used in this paper; In chapter 3, we introduce the results of the second fundamental theorem which applies the knowledge of linear equations and matrices in higher algebra to the difference form of sharing hyperplane in complex projective spaces. The results of this theorem are successfully extended to simple complex variables to complex projective forms. The second fundamental theorem in the difference form of shared hypersurfaces in space and its related conclusions; In chapter 4, some results of the value distribution of solutions of differential difference equations of Fermat type are introduced.
【学位授予单位】：南昌大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O174.52;O175.7
本文编号：2437493
[Abstract]:The second fundamental theorem plays an important role in Nevanlinna's value distribution theory. It can be used to solve many problems in complex differential equation and difference equation, and even to judge the existence and uniqueness of the solution of the equation directly. Therefore, the form of the second fundamental theorem of Nevanlinna's theory is very important. The contents of this dissertation include: chapter 1 introduces the research background and main work of this thesis; the second chapter introduces the basic knowledge of Nevanlinna theory and the related knowledge used in this paper; In chapter 3, we introduce the results of the second fundamental theorem which applies the knowledge of linear equations and matrices in higher algebra to the difference form of sharing hyperplane in complex projective spaces. The results of this theorem are successfully extended to simple complex variables to complex projective forms. The second fundamental theorem in the difference form of shared hypersurfaces in space and its related conclusions; In chapter 4, some results of the value distribution of solutions of differential difference equations of Fermat type are introduced.
【学位授予单位】：南昌大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O174.52;O175.7
【参考文献】
相关期刊论文 前1条
1 WONG Pit-Mann;LAW Hiu-Fai;WONG Philip P.W.;;A Second Main Theorem on P~n for difference operator[J];Science in China(Series A:Mathematics);2009年12期
，本文编号：2437493
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