复线性微分方程的亚纯解及q—平移差分—微分多项式的值分布

发布时间：2018-06-24 04:45

本文选题：复线性微分方程 + 亚纯解　；参考：《江西师范大学》2015年硕士论文

【摘要】：本文运用Nevanlinna值分布理论分别在复平面上和单位圆内研究了几类复线性微分方程亚纯解的增长性和值分布.同时,还研究了一类q-平移差分-微分多项式的值分布.所得结果是对前人已有结果的推广和改进.全文分为四章.第一章,扼要介绍了复线性微分方程值分布理论和复差分与差分方程理论的主要发展线索,同时介绍了本文主要内容和一些基本定义.第二章,在复平面上研究了一类具有Lacunary缺项级数系数的高阶齐次和非齐次线性微分方程亚纯解的[p,q]级和[p,q]下级及解取小函数值点的[p,q]收敛指数和[p,q]下收敛指数.第三章,在单位圆内研究了系数为亚纯函数的齐次和非齐次线性微分方程亚纯解的微分多项式取小函数值点的迭代收敛指数和迭代下收敛指数.第四章,研究了一类正有穷级整函数的q-平移差分-微分多项式的值分布.
[Abstract]:In this paper, the growth and value distribution of meromorphic solutions of some complex linear differential equations are studied on the complex plane and in the unit circle by using Nevanlinna value distribution theory. At the same time, the value distribution of a class of q-translation difference differential polynomials is studied. The result is a generalization and improvement of the previous results. The full text is divided into four chapters. In the first chapter, we briefly introduce the value distribution theory of complex linear differential equation and the main development clue of complex difference and difference equation theory. At the same time, we introduce the main contents and some basic definitions of this paper. In chapter 2, we study the [pnq] convergence index and the convergence index under [pnq] and [pnq] of meromorphic solutions of a class of higher order homogeneous and nonhomogeneous linear differential equations with Lacunary deficient series coefficients on the complex plane. In chapter 3, we study the iterative convergence exponents and the convergence exponents of the meromorphic homogeneous differential equations with meromorphic coefficients and the meromorphic solutions of nonhomogeneous linear differential equations at the point of small function in the unit circle. In chapter 4, we study the value distribution of q-translation differential-differential polynomials for a class of positive finite-order entire functions.
【学位授予单位】：江西师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O174.52

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