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

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.