关于高阶线性复微分方程整函数解的Borel方向

Borel direction of entire function solutions of higher order linear complex differential equation

研究了一类高阶线性非齐次微分方程f_((n))+A_(n-1) f^((n-1))+…+A_(0)f=F的解与自由项F(z)的Borel方向之间的关系,其中A_(0),A_(1),…,A_(n-1)为有限级整函数;并且给出了一类高阶线性齐次方程f^((n))+A_(n-1) f^((n-1))+…+A_(0) f=0的解的Borel方向集合的测度的下界,其中A_(0),A_(1),…,A_(n-1)为整函数且μ(A_(0))>max{ρ(A_(1)),ρ(A_(2)),…,ρ(A_(n))}。

In this paper,we explored the relationship between the solutions of a class of higher order linear non-homogeneous differential equations f_((n))+A_(n-1) f^((n-1))+…+A_(0)f=F and the Borel direction of the free term F(z),where A0,A1,…,An-1 are entire functions of finite order.Besides,we gave the measure lower bound of the Borel direction set of the solutions for a class of higher order linear homogeneous equations f^((n))+A_(n-1) f^((n-1))+…+A_(0) f=0,where A_(0),A_(1),…,A_(n-1)are entire function and μ(A_(0))>max{ρ(A_(1)),ρ(A_(2)),…,ρ(A_(n))}。.