单位圆内高阶齐次线性微分方程解的复振荡  

The Complex Oscllation of Higher Order Homogeneous Linear Differential Equations in the Unit Disc

作　　者：金瑾[1] 

机构地区：[1]毕节学院数学系,贵州毕节551700

出　　处：《山西大同大学学报（自然科学版）》2010年第3期1-5,共5页Journal of Shanxi Datong University(Natural Science Edition)

基　　金：贵州省科学技术基金项目[2010GZ43286];贵州省教育厅资助项目[2007079];毕节学院科研基金资助项目[20072004]

摘　　要：对高阶齐次线性微分方程f(k)(z)+Ak-1(z)f(k-1)(z)+Ak-2(z)f(k-2)(z)+…+A1(z)f′(z)+A0(z)f(z)=0的解进行了研究,其中Aj(z)(j=0,1,2,…,k-1)为单位圆△={z∶|z|<1}内的解析函数,给出了高阶齐次线性微分方程解的增长性与系数增长性之间的关系,并证明了高阶齐次线性微分方程的亚纯可允许解在单位圆内的充满圆序列的存在性.This paper investigates deeply the complex oscillation of higher order homogeneous linear differential equations of the form f（k）（z）＋Ak-1（z）f（k-1）（z）＋Ak-2（z）f（k-2）（z）＋…＋A1（z）f ′（z）＋A0（z）f（z）=0 Where the coefficients are analytic functions in the unit disc Aj（z）（j=0,1,2,…,k-1）,and relations between the growthes of the solu-tion and the coefficeient of higher order homogeneous linear differential equations are given out,and exist of the filling circle align-ment of meromorphic permissble solution of higher order homogeneous linear differential equations are proved in the unit disc.

关 键 词：单位圆 级 解析函数 充满圆 可允许解 

分 类 号：O174.52[理学—数学]