一类高阶线性微分方程亚纯解与小函数的关系
Relation between Meromorphic Solutions of a Class of Higher Order Linear Differential Equations and Functions of Small Growth
DOI: 10.12677/PM.2014.41002, PDF, HTML, 下载: 2,580  浏览: 8,718 
作者: 陈敏风, 陈宗煊:华南师范大学数学科学学院,广州
关键词: 亏值复域微分方程亚纯函数小函数Deficient Value; Complex Differential Equations; Meromorphic Function; Functions of Small Growth
摘要: 本文研究了一类亚纯函数系数高阶齐次和非齐次线性微分方程的亚纯解的增长性,并进一步研究了它们的亚纯解与小函数的关系。其中某一个系数具有有限亏值或满足一定条件,其余系数也满足相应的条件。
Abstract: In this paper, we consider the growth of the meromorphic solutions of a class of higher order homogeneous and non-homogeneous linear differential equations with meromorphic coefficients, and further consider the relation between their meromorphic solutions and functions of small growth, where one of these coefficients has a finite deficient value or satisfies some conditions, others satisfy corresponding conditions.
文章引用:陈敏风, 陈宗煊. 一类高阶线性微分方程亚纯解与小函数的关系[J]. 理论数学, 2014, 4(1): 5-13. http://dx.doi.org/10.12677/PM.2014.41002

参考文献

[1] 杨乐 (1982) 值分布论及其新研究. 科学出版社, 北京.
[2] 仪洪勋, 杨重骏 (1988) 亚纯函数唯一性理论. 科学出版社, 北京.
[3] Gundersen, G. (1988) Finite order solutions of second order linear differential equations. Transactions of the American Mathematical Society, 305, 415-429.
[4] Hellenstein, S., Miles, J. and Rossi, J. (1991) On the growth of solutions of . Transactions of the American Mathematical Society, 324, 693-705.
[5] Wu, P.C. and Zhu, J. (2011) On the growth of solutions of the complex differential equation . Science China Mathematics, 54, 939-947.
[6] 陈宗煊 (1999) 关于高阶线性微分方程亚纯解的增长率. 数学学报, 3, 551-558.
[7] 肖丽鹏, 陈宗煊 (2005) 一类高阶微分方程亚纯解得增长性. 数学研究, 3, 265-271.
[8] Gundersen, G. (1988) Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates. London Mathematical Society, 37, 88-104.
[9] Barry, P.D. (1970) Some theorems related to the theorem. Proceedings of the London Mathematical Society, 21, 334-360.
[10] 陈宗煊 (1996) 二阶亚纯系数微分方程亚纯解的零点. 数学物理学报, 3, 276-283.
[11] Chen, Z.-X. (1994) Zeros of meromorphic solutions of higher order linear differential equations. Analysis, 14, 425-538.
[12] 李锐夫, 戴崇基, 宋国栋 (1988) 复变函数续论. 高等教育出版社, 北京.