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复差分多项式与复线性微分、差分方程亚纯解的一些性质

发布时间:2018-05-02 18:20

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


【摘要】:本文运用Nevanlinna值分布理论及其差分模拟结果研究了复差分多项式与复线性微分、差分方程亚纯解的一些性质,改进并完善了前人的结果.全文分为三章.第一章,简要介绍了复线性微分方程领域和复差分与复差分方程领域的发展历史和本文主要内容,并介绍了复平面上和单位圆内亚纯函数的一些定义和常用记号.第二章,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.分别在复平面上和单位圆内研究了一类具某种特殊解析函数系数的齐次线性微分方程解的迭代级;在复平面上研究了一类具Fabry缺项级数系数或具慢增长性解析函数系数的非首1齐次和非齐次线性微分方程亚纯解的级、超级和解取小函数值点的收敛指数、超收敛指数;在单位圆内研究了一类具慢增长性解析函数系数的齐次和非齐次线性微分方程解的级、M-级、超级和超M-级.第三章,运用Nevanlinna理论的差分模拟结果并结合复线性微分方程的一些研究方法,研究了复线性差分方程和复线性微-差分方程亚纯解及复差分多项式的增长性和值分布.研究了一类具相同增长级系数的齐次线性差分方程亚纯解的级和解取小函数值点的收敛指数;分别研究了多项式系数、超越整函数系数、亚纯函数系数的齐次和非齐次线性微-差分方程亚纯解的级和下级;研究了有限级整函数的差分多项式的零点、取小函数值点和Borel例外值点分布.
[Abstract]:In this paper, some properties of meromorphic solutions of complex difference polynomials and complex linear differential and difference equations are studied by using Nevanlinna value distribution theory and their difference simulation results. The full text is divided into three chapters. In the first chapter, the development history of complex linear differential equations and complex difference and complex difference equations and the main contents of this paper are briefly introduced, and some definitions and commonly used notations of meromorphic functions in complex plane and unit circle are also introduced. In chapter 2, we study the growth and value distribution of meromorphic solutions of some complex linear differential equations on the complex plane and in the unit circle. The iterative order of the solutions of a class of homogeneous linear differential equations with some special analytic function coefficients is studied on the complex plane and in the unit circle respectively. In this paper, we study the order of meromorphic solutions of a class of nonhomogeneous and nonhomogeneous linear differential equations with the coefficients of Fabry deficient series or analytic functions with slow growth on the complex plane. In this paper, we study the order M- order, super and super M- order of solutions of homogeneous and nonhomogeneous linear differential equations with slowly growing analytic function coefficients in a unit circle. In chapter 3, the growth and value distribution of meromorphic solutions and complex difference polynomials of complex linear difference equations and complex linear differential equations are studied by using the difference simulation results of Nevanlinna theory and some research methods of complex linear differential equations. In this paper, we study the convergence exponents of meromorphic solutions of homogeneous linear difference equations with the same growth order coefficients, and study the coefficients of polynomial and transcendental functions, respectively. The order and lower order of meromorphic differential equation with homogeneous and inhomogeneous linear differential-difference equations are studied, the zero points of difference polynomial of finite order integral function are studied, and the distribution of small function value points and Borel exceptional value points are obtained.
【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


本文编号:1834979

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