摘要: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〉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 solutionf≠O of the equation is of infinite order in any angular domain which has λ order Borel direction of B(z) ,and the w order Borel direction of the solution is unanimous with the λ order Borel direction of B(z).