复微分方程整函数解的Julia集的极限方向  

Julia limiting directions of entire solutions of complex differential equations

作　　者：向旭旭 刘建明 王钦 欧阳瑞琦 XIANG Xuxu;LIU Jianming;WANG Qin;OUYANG Ruiqi(School of Mathematical Sciences,Guizhou Normal University,Guiyang 550025,Guizhou,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550025

出　　处：《山东大学学报(理学版)》2024年第12期73-78,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12261023;11861023);贵州师范大学学术新苗培养及创新探索专项资助项目(黔科合平台人才[2018]5769-05)。

摘　　要：利用Phragmén-Lindelöf指标函数以及完全正规增长整函数的性质研究微分方程f(n)+Pn-1(z)f(n-1)++P0(z)f=0和f″+A(z)f′+B(z)f=0整函数解的Julia集的极限方向,获得方程无穷级整函数解及其导数和原函数的公共Julia集的极限方向集测度的下界估计,其中n≥2,Pj(z)(j=1,2,…,n-1)是整函数,P0(z)､A(z)和B(z)为完全正规增长的整函数。The Julia limiting directions of entire solutions of complex differential equations f(n)+Pn-1(z)f(n-1)++P0(z)f=0 and f″+A(z)f′+B(z)f=0 are studied by using Phragmén-Lindelöf indicator function and the properties of the completely regular growth functions,the lower bound of the measure of the set of common Julia limiting directions of the derivatives and primitives of infinite order entire solutions of the equations mentioned above is obtained,where n≥2,Pj(z)(j=1,2,…,n-1)are entire functions,P0(z),A(z)and B(z)are entire functions of completely regular growth.

关 键 词：复微分方程 Julia集的极限方向 Phragmén-Lindelöf指标函数 完全正规增长 

分 类 号：O174.52[理学—数学]