| 某类高阶周期线性微分方程解的性质 |
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| 引用本文： | 朱丹晓,陈宗煊. 某类高阶周期线性微分方程解的性质[J]. 数学杂志, 2012, 32(2): 307-317 |
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| 作者姓名： | 朱丹晓 陈宗煊 |
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| 作者单位： | 华南师范大学数学科学学院,广东广州,510631 |
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| 摘 要： | 本文研究了一类高阶周期系数线性微分方程解的性质问题. 利用复分析的相关理论和方法, 获得了在一些假设条件下, 当方程的系数 As 起控制作用时, 方程 f(k) + Ak-2f(k-2) + ...+Asf(s) + ... + A0f = 0 的任意两个线性无关解 f1,f2 满足λe(f1f2) ≥σe(As) 的结果, 推广了肖丽鹏的一个结果.
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| 关 键 词： | 周期线性微分方程 e-型级 e-型零点收敛指数 线性无关 |
ON COMPLEX OSCILLATION PROPERTY OF SOLUTIONS FOR HIGHER-ORDER PERIODIC DIFFERENTIAL EQUATIONS |
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| ZHU Dan-xiao , CHEN Zong-xuan. ON COMPLEX OSCILLATION PROPERTY OF SOLUTIONS FOR HIGHER-ORDER PERIODIC DIFFERENTIAL EQUATIONS[J]. Journal of Mathematics, 2012, 32(2): 307-317 |
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| Authors: | ZHU Dan-xiao CHEN Zong-xuan |
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| Affiliation: | (School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China) |
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| Abstract: | In this article,we investigate properties of solutions for higher-order periodic differential equations.By using theory and method of complex analysis,we obtain that under certain condition,when As of equation f(k) + Ak-2f(k-2) +...+ Asf(s) +...+ A0f = 0 is the dominant coefficient,the e-type convergence exponent of zeros of the product of its two linearly independent solutions satisfies λe(f1f2) ≥ σe(As).The results obtained are generalization of a result due to Xiao Lipeng. |
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| Keywords: | periodic differential equation e-type order e-type exponent of convergence linearly independent. |
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