高阶齐次复线性微分方程解的[p,q],φ级  

[p,q],φ-Order of Solutions of Higher-Order Homogeneous Complex Linear Differential Equations

作　　者：龚攀[1] 涂金[2] GONG Pan;TU Jin(School of Mathematics and Computational Science,Shangrao Normal University,Shangrao 334001,China;School of Mathematics and Statistics,Jiangxi Normal University,Nanchang 330022,China)

机构地区：[1]上饶师范学院数学与计算科学学院,江西上饶334001 [2]江西师范大学数学与统计学院,江西南昌330022

出　　处：《数学的实践与认识》2025年第3期211-223,共13页Mathematics in Practice and Theory

基　　金：国家自然科学基金(12161074,12163003);江西省教育厅科学技术研究项目(GJJ2401702)。

摘　　要：研究高阶齐次线性微分方程f^(k)+A_(k-1)(z)f^(k-1)+…+A_(1)(z)f′+A_(0)(z)f=0解的增长性与其系数的增长性的关系,其中系数A_(j)(z)(j=0,1,…,k-1)是复平面C内的整函数.得到了一些关于[p,l],φ级和[p,q],φ下级的相关定理,丰富和完善了前人的一些结论.In this paper,we study the growth relationship between the solutions and the coefficients of higher-order homogeneous linear differential equation f^(k)+A_(k-1)(z)f^(k-1)+…+A_(1)(z)f′+A_(0)(z)f=0,where the coefficients A_(j)(z)(j=0,1,…,k-1)are entire functions in the complex plane C.We obtain some theorems on the[p,d],φ-order and on the lower[p,q],φ-order,which are generalizations and improvements of some previous theorems.

关 键 词：线性微分方程 整函数 [p q] φ级 [p q] φ型 

分 类 号：O174.52[理学—数学]