高阶线性微分方程的解在角域内的增长性及Borel方向

The Growth and Borel Direction of Solutions of Higher Order Linear Differential Equation in Angular Domains

主要运用角域上的值分布理论和方法,研究了整系数高阶线性微分方程f(n)+An-1f(n-1)+…+A0f=0的解在角域内的增长性和Borel方向.假定Aj(0≤j≤n-1)满足某些条件,证明了方程的非零解在含有A0的λ(λ>0)级Borel方向的任意角域内的增长级为无穷,且非零解的无穷级Borel方向与A0的λ级Borel方向一致.

By using the fundamental theory and method of value distribution in angular domain,it is investigated that growth and Borel direction of solutions in angular domains of the higher order linear differential equation f（n）＋ A n-1 f（n-1）＋ … ＋ A 0 f = 0 where A j（j =0,…,n-1） are entire functions.Given some conditions for the coefficients A j（0≤j≤n-1）,it is proved that every solution f0 of the equation is of the infinite order in any angular domain which has λ order Borel direction of A 0,and the ∞ order Borel direction of the solution is unanimous with the λ order Borel direction of A0.