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(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）.
出处
《江西师范大学学报（自然科学版）》
CAS
北大核心
2013年第1期1-5,共5页
Journal of Jiangxi Normal University(Natural Science Edition)
基金
国家自然科学基金(11171170)资助项目
关键词
微分方程
解
角域
BOREL方向
无穷级
differential equations
solutions
angular domain
Borel direction
infinite order
