[1]易才凤,刘旭强.方程f″+Af'+Bf=0的解在角域内的增长性及Borel方向[J].江西师范大学学报(自然科学版),2013,(01):1-5.
　YI Cai-feng,LIU Xu-qiang.The Growth and Borel Direction of Solutions for Differential Equation f" + Af' + Bf =0 in Angular Domains[J].Journal of Jiangxi Normal University:Natural Science Edition,2013,(01):1-5.
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方程f″+Af'+Bf=0的解在角域内的增长性及Borel方向()
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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:
2013年01期
页码:
1-5
栏目:
出版日期:
2013-01-01

文章信息/Info

Title:
The Growth and Borel Direction of Solutions for Differential Equation f" + Af' + Bf =0 in Angular Domains
作者:
易才凤;刘旭强
江西师范大学数学与信息科学学院,江西南昌,330022
Author(s):
YI Cai-feng；LIU Xu-qiang
关键词:
微分方程; 解; 角域; Borel方向; 无穷级
Keywords:
differential equations;  solutions;  angular domain;  Borel direction;  infinite order
分类号:
O174.52
文献标志码:
A
摘要:
运用角域内值分布的理论和方法,研究了整系数2阶线性微分方程f”+Af’+Bf=0的解在角域内的增长性和Borel方向.在给定条件下,证明了方程的每一非零解在含有B的λ(λ＞0)级Borel方向的任意角域内的增长级均为无穷,且B的λ级Borel方向与解的无穷级Borel方向一致.
Abstract:
The growth and Borel direction of solutions in angular domains for differential equation f ″+Af '+Bf=0 is investigated where A(z) and B(z) are entire functions,by using the fundamental theory and method of value distribution in angular domain.Under some conditions,it is proved that every solution f0 of the equation is of infinite order in any angular domain which has λ order Borel direction of B(z),and the ∞order Borel direction of the solution is unanimous with the λ order Borel direction of B(z).

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备注/Memo

备注/Memo:
国家自然科学基金(11171170)
更新日期/Last Update: 1900-01-01