方程f″+Af'+Bf=0的解在角域内的增长性及Borel方向
The Growth and Borel Direction of Solutions for Differential Equation f" + Af' + Bf =0 in Angular Domains

运用角域内值分布的理论和方法,研究了整系数2阶线性微分方程f”+Af’+Bf=0的解在角域内的增长性和Borel方向.在给定条件下,证明了方程的每一非零解在含有B的λ(λ＞0)级Borel方向的任意角域内的增长级均为无穷,且B的λ级Borel方向与解的无穷级Borel方向一致.
The growth and Borel direction of solutions in angular domains for differential equation f ″+Af '+Bf=0 is investigated where A(z) and B(z) are entire functions,by using the fundamental theory and method of value distribution in angular domain.Under some conditions,it is proved that every solution f??0 of the equation is of infinite order in any angular domain which has λ order Borel direction of B(z),and the ∞order Borel direction of the solution is unanimous with the λ order Borel direction of B(z)