江西科学2024,Vol.42Issue(6) :1141-1147.DOI:10.13990/j.issn1001-3679.2024.06.002

单位圆内某类高阶微分方程解的增长性

The Growth of Solutions for Some Kind of Higher Order Differential Equations in the Unit Disc

龚攀 吴红星
江西科学2024,Vol.42Issue(6) :1141-1147.DOI:10.13990/j.issn1001-3679.2024.06.002

单位圆内某类高阶微分方程解的增长性

The Growth of Solutions for Some Kind of Higher Order Differential Equations in the Unit Disc

龚攀 1吴红星1
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作者信息

  • 1. 上饶师范学院数学与计算科学学院,334001,江西,上饶
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摘要

研究高阶齐次线性微分方程f(n)+An-1(z)f(n-1)+…+A1(z)f'+A0(z)f=0解的增长性,其中系数是单位圆Δ内的解析函数.当A0(z)和As(z)的[p,q]下级,[p,q]下型或者[p,q]下新型控制其他的系数,得到了解的[p,q]级的估计.

Abstract

The paper studies the growth of solutions to the higher order homogeneous linear differential equation,f(n)+An-1(z)f(n-1)+…A1(z)f'+A0(z)f=0 where the coefficients are analytic functions in the unit disc Δ.When A0(z)and As(z)dominate the other coefficients,we obtain some estimates of[p,q]-orderof solutions of the equation by using the lower[p,q]-order,the lower[p,q]-type or the lower new[p,q]-type of A0(z)to As(z).

关键词

单位圆/解析系数/[p,q]新型

Key words

unit disc/analytic coefficients/new[p,q]-type

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出版年

2024
江西科学
江西省科学院

江西科学

影响因子:0.286
ISSN:1001-3679
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