微分方程解的复振荡及亚纯函数唯一性定理

发布时间：2018-06-12 13:52

  本文选题：微分方程 + 亚纯函数　； 参考：《江西师范大学》2015年硕士论文

【摘要】：本文主要研究高阶线性微分方程解的复振荡性质及亚纯函数分担一个公共小函数的唯一性问题.全文共分四章.第一章,简要介绍研究内容的背景知识和相关预备理论知识,侧重介绍Nevanl lnna理论中的一些基本结果,它们是研究微分方程复振荡理论和亚纯函数唯一性理论的重要工具.第二章,研究了一类整函数系数高阶齐次线性微分方程解的零点分布.利用Ne vanlinna值分布理论,得到当系数Ak-1的增长性起主要支配作用时,方程f(κ)+Aκ-1f(κ-1)+…+Aof=0任意超越解的零点收敛指数为无穷.第三章,研究了亚纯系数高阶线性微分方程f(κ)+Aκ-1f(κ-1)+…+Aof=0解的增长性.证明了如果Ao(z)以∞为亏值,Aj(z)(0≤j≤k-1)满足某些条件,则上述方程的每个非零亚纯解都为无穷级,并得到非零亚纯解的超级的下界估计.第四章,研究了亚纯函数(或整函数)关于微分多项式弱分担一个多项式的唯一性问题,得到两个亚纯函数唯一性定理,推广了Li和Yi.Chen和Zhang所得结裂.
[Abstract]:In this paper, we study the complex oscillatory properties of solutions of higher order linear differential equations and the uniqueness of meromorphic functions sharing a common small function. The full text is divided into four chapters. In the first chapter, we briefly introduce the background knowledge and the related presupposition theory of the research content, focusing on some basic results of Nevanl lnna theory, which are important tools for studying the complex oscillation theory of differential equations and the uniqueness theory of meromorphic functions. In chapter 2, the zero distribution of solutions for a class of high order homogeneous linear differential equations with whole function coefficients is studied. By using the distribution theory of ne vanlinna value, the equation f (魏) A 魏 -1f (魏 -1) is obtained when the growth of coefficient Ak-1 plays a dominant role. The zero convergence exponent of Aof=0 's arbitrary transcendental solution is infinite. In chapter 3, we study the meromorphic coefficient higher order linear differential equation f (魏) A 魏 -1 f (魏 -1). The growth of Aof=0 solution. It is proved that every nonzero meromorphic solution of the above equation is of infinite order if Aoz) satisfies some conditions by using 鈭，

本文编号：2009893