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应用数学学报  2013, Vol. 36 Issue (5): 851-861    DOI:
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关于高阶线性微分方程解的增长性
蓝双婷, 陈宗煊
华南师范大学数学科学学院, 广州 510631
On the Growth of Solutions of Higher Order Differential Equation
LAN Shuangting, CHEN Zongxuan
School of Mathematical Sciences, South China Normal University, Guangzhou 510631
 全文: PDF (307 KB)   HTML (1 KB)   输出: BibTeX | EndNote (RIS)      背景资料
摘要 在本文中, 我们研究了一类高阶齐次线性微分方程
f(k)+Ak-1f(k)-1+...+A0f=0,
其中Aj(z) (j=0,1,...,k-1) 是有限级整函数, 且存在As(z)(s∈{0,1,...,k-1}) 是超越的且 σ(As)<1/2或其泰勒展式为缺项级数. 我们给出了方程任一解 f0 的增长估计.
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蓝双婷
陈宗煊
关键词亏量   缺项级数   超级     
Abstract: In this paper, we consider higher order differential equation
f(k)+Ak-1f(k)-1+...+A0f=0,
where Aj(z) (j=0,1,...,k-1) are entire functions of finite order, such that there is some As(z)(s∈{0,1,...,k-1}) being transcendental with σ(As)<1/2 or a Fabry power series. We give the estimation of the growth of every solution f0 of the equation above.
Key wordsdeficient value   fabry power series   hyper order   
收稿日期: 2011-12-08;
基金资助:

国家自然科学基金 (No.11171119)和国家天元基金(No. 11226090)资助项目.

引用本文:   
蓝双婷,陈宗煊. 关于高阶线性微分方程解的增长性[J]. 应用数学学报, 2013, 36(5): 851-861.
LAN Shuangting,CHEN Zongxuan. On the Growth of Solutions of Higher Order Differential Equation[J]. Acta Mathematicae Applicatae Sinica, 2013, 36(5): 851-861.
 
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