高阶复线性微分方程整函数解的Borel方向  

Borel direction of integral function solutions for higher order complex linear differential equations

作　　者：李静静 黄志刚 LI Jingjing;HUANG Zhigang(School of Mathematical Sciences,SUST,Suzhou 215009,China)

机构地区：[1]苏州科技大学数学科学学院,江苏苏州215009

出　　处：《苏州科技大学学报（自然科学版）》2022年第2期9-14,共6页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11001057)。

摘　　要：利用Nevanlinna角域值分布理论,研究了线性微分方程f^((n))+A_(n-1)f^((n-1))+…+A_(1)f′+A_(0)f=F的解f(z)的Borel方向的存在性与F(z)的Borel方向的关系,其中A_(0),A_(1),…,A_(n-1)是有限级整函数,F(z)是超越整函数。证明了线性微分方程f^((n))+e^(c_(n-1)z)f^((n-1))+…+e^(c_(n)z)f′+e^(c_(0)z)f=0的非零解f(z)的Borel方向测度有下界。Using Nevanlinna angle domain value distribution theory,we explored the relationship between the existence of the Borel direction of the solution f(z)for linear differential equation f^((n))+A_(n-1)f^((n-1))+…+A_(1)f′+A_(0)f=F and the Borel direction of F(z),where A_(0),A_(1),…,A_(n-1) are integral functions of finite order and F(z)are transcendental integral functions.And we proved that the Borel direction measure of the nonzero solution f(z)of the linear differential equation f^((n))+e^(c_(n-1)z)f^((n-1))+…+e^(c_(n)z)f′+e^(c_(0)z)f=0 has a lower bound.

关 键 词：BOREL方向 整函数 线性微分方程 测度 

分 类 号：O174.52[理学—数学]