线性微分方程的系数及解的增长性估计  

The coefficients of linear differential equations and the estimation of growth order of solutions

作　　者：张建军[1] 戚建明[1] 袁文俊[1] 

机构地区：[1]广州大学数学与信息科学学院,广东广州510006

出　　处：《广州大学学报（自然科学版）》2007年第3期15-18,共4页Journal of Guangzhou University:Natural Science Edition

基　　金：国家自然科学基金资助项目(10471028);广州市教育局科技计划项目(20062025)

摘　　要：对次数至少有一个不小于零的有理函数系数齐次线性微分方程,给出了方程所有亚纯解的级中最大的级的增长性估计,同时对方程的系数为多项式的情形,证明了一个与Hellerstein-Rossi猜想有关的结果.This paper gives an estimation of maximal order of all the meromorphic solutions of the homogeneous linear differential equation with rational function coefficients, under the assumption that the degree is greater than or equal to zero for at least one coefficient, and also gives a result which is related to Hellerstein-Rossi conjecture when the coefficients are polynomials.

关 键 词：线性微分方程 亚纯函数 零点 级 

分 类 号：O174.5[理学—数学]