江西师范大学学报(自然科学版)
江西師範大學學報(自然科學版)
강서사범대학학보(자연과학판)
JOURNAL OF JIANGXI NORMAL UNIVERSITY(NATURAL SCIENCES EDITION)
2014年
4期
399-402
,共4页
整函数%杨-张不等式%微分方程%无穷级
整函數%楊-張不等式%微分方程%無窮級
정함수%양-장불등식%미분방정%무궁급
entire function%Yang-Zhang inequality%differential equations%infinite order
运用 Nevanlinna 值分布的基本理论和整函数的相关性质,研究了一类高阶齐次线性微分方程解的增长性,在假设其系数均为整函数,且有1个满足杨-张不等式的极端情况的条件下,证明了方程的每1个非零解均具有无穷级。
運用 Nevanlinna 值分佈的基本理論和整函數的相關性質,研究瞭一類高階齊次線性微分方程解的增長性,在假設其繫數均為整函數,且有1箇滿足楊-張不等式的極耑情況的條件下,證明瞭方程的每1箇非零解均具有無窮級。
운용 Nevanlinna 치분포적기본이론화정함수적상관성질,연구료일류고계제차선성미분방정해적증장성,재가설기계수균위정함수,차유1개만족양-장불등식적겁단정황적조건하,증명료방정적매1개비영해균구유무궁급。
By using the fundamental theory of value distribution of Nevanlinna and the property of entire function, the growth of solutions of the higher order linear differential equations is considered where coefficients are entire function. Assume that one of coefficients is extremal for Yang-Zhang inequality,it was proved that every nontrivial solution of the complex differential equation has infinite order.