【作者】 曹廷彬；

【导师】 陈宗煊；

【作者基本信息】 江西师范大学 ， 基础数学， 2004， 硕士

【摘要】 本文利用亚纯函数的迭代级的概念，研究了迭代级亚纯函数的Borel方向及其微分方程解的复振荡理论。全文共分四章。 第一章介绍了迭代级亚纯函数及其相关定义。第二章，我们证明了迭代级亚纯函数的Borel例外值、充满圆及Borel方向。推广了已有的结果。 本文中，我们讨论了迭代级亚纯函数系数线性微分方程解的性质。其中第三章研究了一类高阶线性齐次与非齐次迭代级整函数系数微分方程解的增长性问题。当存在某个系数或自由项对方程解的性质起主要支配作用时，得到了方程解的迭代级及其零点的迭代收敛指数的精确估计。第四章研究了高阶线性齐次与非齐次迭代级亚纯函数系数微分方程，获得了关于亚纯函数解的迭代增长级，迭代收敛指数的几个结果。推广了已有的结果。更多还原

【Abstract】 In this thesis, we investigate the Borel direction of the meromorphic functions with iterated order and the complex oscillation theory of solutions of differential equations by using the concept of iterated order. It includes following four chapters.In chapter 1, we introduce the definitions concerning iterated order of meromorphic function. In chapter 2, we investigate the Borel exceptional values, full circles, and Borel directions of iterated order of meromorphic functions .In this thesis, we investigate the property of solutions of differential equations with coefficients of iterated order. In chapter 3. we investigate growth problems of solutions of one type of homogeneous and non-homogeneous higher order linear differential equations with entire coefficients of iterated order. For this type of equations, we obtain precise estimate of iterated order and iterated covergence exponent of the zeros of solutions when some coefficient or free term is main dominating to the properties of the solutions. In chapter 4 , we investigate complex homogenous and non-homogeneous higher order linear differential equations with meromorphic coefficients of iterated order. We obtain several results concerning the iterated order of meromorphic solutions, and the iterated convergence exponent of the zeros of meromorphic solutions. We also improve the results obtained by some authors.更多还原