线性微分方程解在角域内的性质  

THE PROPERTIES OF SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS IN ANGULAR DOMAIN

作　　者：魏文龙 魏冬梅 黄志刚[1] WEI Wen-long;WEI Dong-mei;HUANG Zhi-gang(School of Mathematics and Physics,Suzhou University of Science and Technology,Suzhou 215009,China)

机构地区：[1]苏州科技大学数理学院,江苏苏州215009

出　　处：《数学杂志》2019年第2期269-278,共10页Journal of Mathematics

基　　金：国家自然科学基金(11001157);江苏省自然科学基金(BK2010234);苏州科技大学研究生科研创新计划项目(SKYCX16-007)

摘　　要：本文主要研究了线性微分方程f″+A(z)f′+B(z)f=F(z)解的精确级Borel方向的问题.利用熊庆来的无限级型函数和庄圻泰的关于无穷级Borel方向的一个等价条件,获得了方程非齐次项的精确级Borel方向就是方程解的精确级Borel方向的结果,推广了已有的结论.In this paper,we mainly study the problem on the Borel directions of precise order of solutions of linear differential equations f″+A(z)f′+B(z)f=F(z).By using the infinity order type function of Xiong Qinglai and a sufficient and necessary condition for infinity order Borel direction which was established by Chuang Chatai,we obtain the result that the Borel directions of precise order of solutions of linear differential equations also belongs to F(z)which generalizes the previously results.

关 键 词：亚纯函数 BOREL方向 零点聚值线 精确级 

分 类 号：O174.52[理学—数学]