一类复系数微分方程解的增长性

安蕾,肖丽鹏

(江西师范大学数学与信息科学学院,江西 南昌 330022)

一类复系数微分方程解的增长性

安蕾,肖丽鹏

(江西师范大学数学与信息科学学院,江西 南昌 330022)

研究了一类系数是亚纯函数的高阶微分方程解的性质,假设其中某一个系数具有有限亏值,然后对其它的系数添加相应的限制条件,使得方程的每一个非零亚纯解都具有无穷级.

亏值;复系数微分方程;亚纯函数;无穷级

1 引言与结果

2 引理

3 定理的证明

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On the growth of solutions to the complex di ff erential equation

An Lei,Xiao Lipeng
(Institute of Mathematics and Information Science,Jiangxi Normal University,Nanchang 330022,China)

In this paper,we consider the higher order linear di ff erential equation with meromorphic coefficients. Assume one of these coefficients has a fi nite de fi cient value,then we will give some conditions on others which can guarantee that every meromorphic solution of the equation has in fi nite order.

de fi cient value,complex di ff erential equations,meromorphic function,in fi nite order

O174.52

A

1008-5513(2012)05-0659-09

2012-06-15.

国家自然科学基金(11126144,11171119);江西省教育厅青年科学基金(GJJ12207).

安蕾(1987-),硕士生,研究方向：复分析.

2010 MSC:30D35,34A20