一類復(fù)系數(shù)微分方程解的增長性

安蕾,肖麗鵬

(江西師范大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院,江西 南昌 330022)

一類復(fù)系數(shù)微分方程解的增長性

安蕾,肖麗鵬

(江西師范大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院,江西 南昌 330022)

研究了一類系數(shù)是亞純函數(shù)的高階微分方程解的性質(zhì),假設(shè)其中某一個系數(shù)具有有限虧值,然后對其它的系數(shù)添加相應(yīng)的限制條件,使得方程的每一個非零亞純解都具有無窮級.

虧值;復(fù)系數(shù)微分方程;亞純函數(shù);無窮級

1 引言與結(jié)果

2 引理

3 定理的證明

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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.

國家自然科學(xué)基金(11126144,11171119);江西省教育廳青年科學(xué)基金(GJJ12207).

安蕾(1987-),碩士生,研究方向：復(fù)分析.

2010 MSC:30D35,34A20