[1]石磊,易才凤.一类高阶线性微分方程解的增长性[J].江西师范大学学报(自然科学版),2012,(03):230-233.
 SHI Lei,YI Cai-feng.The Growth of Solutions for a Class Higher Order Linear Differential Equations[J].,2012,(03):230-233.
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一类高阶线性微分方程解的增长性()
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《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2012年03期
页码:
230-233
栏目:
出版日期:
2012-05-01

文章信息/Info

Title:
The Growth of Solutions for a Class Higher Order Linear Differential Equations
作者:
石磊;易才凤
江西师范大学数学与信息科学学院,江西南昌330022
Author(s):
SHI Lei YI Cai-feng
关键词:
微分方程整函数亏值无穷级
Keywords:
differential equations entire function deficient value infinite order
分类号:
O174.52
文献标志码:
A
摘要:
利用 Nevanlinna 的基本理论和方法,研究了齐次线性微分方程() f k+A f k k??11++=及非齐次Af 0线性微分方程解的增长性.在假设存在某个(1 A s s k ?≤≤1)具有有限亏值的有限级整函数的情况下,证明了齐次线性微分方程的任一非零解均为无穷级,非齐次方程除1个例外解外,其它的非零解也均为无穷级
Abstract:
By using the fundamental theory and method of Nevanlinna, the growth of solutions of the homogeneous linear differential equation and non-homogeneous linear differential equation was investigated. Assuming some is entire functions with a finite deficient value, it was proved that every solution f ≡/ 0 of the homogeneous differential equation has infinite order. Furthermore, the solutions f ≡/ 0 of non-homogeneous linear differential equation have the same property except for an extra solution.

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更新日期/Last Update: 1900-01-01