【作者】 朱军；

【导师】 伍鹏程；

【作者基本信息】 贵州师范大学 ， 计算数学， 2009， 硕士

【摘要】 本文主要研究亚纯函数系数微分方程解的复振荡,分别考虑一类高阶情形和一类二阶情形。全文共分为四个部分。第一部分(引言)介绍了国内外研究现状,并引入了一些相关定义和记号,及本文所要解决的问题。第二部分(第二章)考察了Kwon Ki-Ho关于二阶整函数系数微分方程所得的结果,在一定条件下,得到了二阶亚纯函数系数情形的部分结论。第三部分(第三章)考察Kwon Ki-Ho关于二阶整函数系数微分方程解的增长性研究。对方程的某个系数作适当限制后,得出高阶亚纯函数系数情形的类似结论。第四部分(第四章)研究了一类高阶亚纯函数解的增长性,在一定程度上改进了陈宗煊,肖丽鹏等的结果,得到了高阶线性微分方程亚纯解级的精确估计。更多还原

【Abstract】 In this paper,we mainly study the complex oscillation of solutions of differential equations on meromorphic function coefficients,and respectively consider two kinds of equations,including the second order and the higher order.It includes the following four parts.In part 1(Introduction),we give an introduction of present situation of this field in domestic and foreign,bright in some related definitions and signs,and give the questions that in this paper will be considered.In part 2(Chapter 2),we study the result made by Kwon Ki-Ho of the second order differential equations on entire function coefficients.In some conditions,we obtain the similar parts of conclusions of the second order differential equations on meromorphic function coefficients.In part 3(Chapter 3),we investigate the growth of solutions of the second order differential equations on entire function coefficients.We obtain the similar conclusion of higher order differential equations on meromorphic function coefficients,when some coefficients of equations satisfy some special conditions.In part 4(Chapter 4),we study the growth of solutions of one kind of higher order differential equations on meromorphic function coefficients.To some extent,we improve the result made by Chen ZongXuan and Xiao LiPeng,and we obtain the precise estimations of meromorphic solutions of the equations on higher order linear differential equations.更多还原