| 一类整函数系数微分方程解的复振荡 |
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| 引用本文： | 江良英,陈宗煊. 一类整函数系数微分方程解的复振荡[J]. 数学研究及应用, 2006, 26(3): 517-524 |
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| 作者姓名： | 江良英 陈宗煊 |
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| 作者单位： | 1. 江西师范大学数学与信息科学学院,江西,南昌,330037
2. 华南师范大学数学系,广东,广州,510631 |
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| 基金项目： | 国家自然科学基金(10161006)，广东省自然科学基金(04010360) |
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| 摘 要： | 本文研究了微分方程f~(k) A_((k-1))f~((k-1)) … A_0f=F(k≥2)解的增长级和零点收敛指数,其中A_j=B_je~(P_j),j=0,1,…,k-1,B_j(z)为整函数,P_j(z)为多项式,σ(B_j)＜degP_j．
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| 关 键 词： | 微分方程 整函数 增长级 零点 收敛指数 |
| 文章编号： | 1000-341X(2006)03-0517-08 |
| 收稿时间： | 2004-07-05 |
| 修稿时间： | 2004-07-05 |
The Complex Oscillation of a Class of Linear Differential Equation with Entire Coefficients |
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| JIANG Liang-ying and CHEN Zong-xuan. The Complex Oscillation of a Class of Linear Differential Equation with Entire Coefficients[J]. Journal of Mathematical Research with Applications, 2006, 26(3): 517-524 |
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| Authors: | JIANG Liang-ying and CHEN Zong-xuan |
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| Affiliation: | School of Math. & Infor., Jiangxi Normal University, Nanchang 330027, China;Dept. of Math., South China Normal University, Guangzhou 510631, China |
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| Abstract: | This paper deals with the orders and zeros of the solutions of the differential equation $f^{(k)}+A_{k-1}f^{(k-1)}+cdots+A_0f=F, kge2,$ where $A_j=B_je^{P_j},j=0,1,cdots,k-1,B_j(z)$ are entire functions, $P_j(z)$ are polynomials, and $sigma(B_j)<{rm deg}P_j$. |
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| Keywords: | linear differential equation entire functions order zero exponent of convergence. |
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