高阶非齐次线性微分方程解的增长级  

Growth of Solutions of Non-Homogeneous Higher Order Linear Differential Equations

作　　者：周鉴 龙见仁 

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550001

出　　处：《中北大学学报（自然科学版）》2017年第5期544-548,共5页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11501142);贵州省科学技术基金(黔科合J字LKS[2009]04号)

摘　　要：运用微分方程复振荡的理论,研究一类具有整函数系数的高阶非齐次复线性微分方程解的增长级,其中方程的系数均为整函数且非齐次项不恒为零.当方程的系数增长级满足一定的条件时,方程任一非零解具有无穷增长级.This paper concerned with the growth of solutions of the non-homogeneous higher order linear differential equations with entire function coefficients by using complex oscillation theory of linear differential equations,where the coefficients are entire functions and the non-homogeneous term unequal to zero.It is shown when the coefficients order meets certain conditions then every non-zero solution of the equation is of infinite order.

关 键 词：线性微分方程 增长级 整函数 零点收敛指数 

分 类 号：O174.52[理学—数学]