| 线性微分方程的系数及解的增长性估计 |
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| 引用本文： | 张建军,戚建明,袁文俊.线性微分方程的系数及解的增长性估计[J].广州大学学报(自然科学版),2007,6(3):15-18. |
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| 作者姓名： | 张建军 戚建明 袁文俊 |
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| 作者单位： | 广州大学,数学与信息科学学院,广东,广州,510006 |
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| 基金项目： | 国家自然科学基金
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广东省广州市教育局资助项目 |
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| 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.
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| 关 键 词： | 线性微分方程 亚纯函数 零点 级 |
| 文章编号： | 1671-4229（2007）03-0015-04 |
| 修稿时间： | 2006-09-272006-11-30 |
The coefficients of linear differential equations and the estimation of growth order of solutions |
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| ZHANG Jian-jun,QI Jian-ming,YUAN Wen-jun.The coefficients of linear differential equations and the estimation of growth order of solutions[J].Journal og Guangzhou University:Natural Science Edition,2007,6(3):15-18. |
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| Authors: | ZHANG Jian-jun QI Jian-ming YUAN Wen-jun |
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| Institution: | School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China |
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| Abstract: | 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. |
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| Keywords: | linear differential equation meromorphic function zero order |
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