【作者】 陈玉；

【导师】 陈宗煊；

【作者基本信息】 江西师范大学 ， 应用数学， 2006， 硕士

【摘要】 本文运用复分析的理论和方法，研究了几种类型的线性微分方程解的性质。本文共分五部分： 第一部分：概述了本研究领域的发展历史。 第二部分：引入一些预备知识，主要是后几章要用到的一些概念的定义、记法，以方便读者阅读。 第三部分：研究了一类高阶整函数系数线性微分方程解的复振荡性质，得到了方程解的增长级的精确估计，推广了已有的结果。 第四部分：研究了几种类型的高阶亚纯函数系数线性微分方程解的复振荡性质，得到了方程亚纯解的增长率的精确估计。把已有的结果由整函数系数方程推广到了亚纯函数系数方程。 第五部分：研究了一类亚纯函数系数的二阶线性微分方程的亚纯解及其一阶和二阶导数的不动点及超级问题，得到了有关复域微分方程亚纯解及其一阶和二阶导数的不动点性质，更多还原

【Abstract】 Content:In this thesis,we investigate the complex oscillation properties of the solutions of some types of linear differential equations by applying the theories and methods of the complex analysis.lt contains the following five parts:In part 1, we give a brief introduction of history on development of this research field.In part 2,we introduce some preliminary knowledge,which is mainly definitions and marks of some concepts used in later chapters.In part 3, we investigate the property of complex oscillation of the solutions of a type of higher-order linear differential equation with entire coefficients. We obtain some precise estimates of the growth of the solutions of the equation and improve the result obtained before.In part 4,we investigate the property of complex oscillation of the solutions of some types of higher-order linear differential equations with meromorphic coefficients.We obtain some precise estimates of the growth of the meromorphic solutions of the equations,and improve the results of the equations with entire coefficients to the equations with meromorphic coefficients.In part 5,we investigate the problems on the fixed points and hyper order of solutions and their 1^st,2^nd derivatives of a class of second order linear differential equations with meromorphic coefficients. We obtain the precise properties of fixed points of meromorphic solutions of complex differential equations.更多还原