| 二阶周期线性微分方程解的几个性质 |
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| 引用本文： | 肖丽鹏,陈宗煊. 二阶周期线性微分方程解的几个性质[J]. 数学研究及应用, 2011, 31(2): 279-286. DOI: 10.3770/j.issn:1000-341X.2011.02.011 |
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| 作者姓名： | 肖丽鹏 陈宗煊 |
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| 作者单位： | 江西师范大学数学与信息科学学院, 江西 南昌 330022;华南师范大学数学科学学院, 广东 广州 510631 |
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| 基金项目： | 国家自然科学基金(Grant No.10871076),江西师范大学博士启动基金(Grant No.2614). |
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| 摘 要： | In this paper,the zeros of solutions of periodic second order linear differential equation y ＋ Ay = 0,where A（z） = B（e z ）,B（ζ） = g（ζ） ＋ p j=1 b ？j ζ ？j ,g（ζ） is a transcendental entire function of lower order no more than 1/2,and p is an odd positive integer,are studied.It is shown that every non-trivial solution of above equation satisfies the exponent of convergence of zeros equals to infinity.
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| 关 键 词： | periodic differential equation complex oscillation regular order of growth |
| 收稿时间： | 2009-03-01 |
| 修稿时间： | 2009-10-14 |
Some Properties of Solutions of Periodic Second Order Linear Differential Equations |
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| Li Peng XIAO and Zong Xuan CHEN. Some Properties of Solutions of Periodic Second Order Linear Differential Equations[J]. Journal of Mathematical Research with Applications, 2011, 31(2): 279-286. DOI: 10.3770/j.issn:1000-341X.2011.02.011 |
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| Authors: | Li Peng XIAO and Zong Xuan CHEN |
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| Affiliation: | 1. Institute of Mathematics and Informations, Jiangxi Normal University, Jiangxi 330022, P. R. China
2. School of Mathematical Science, South China Normal University, Guangdong 510631, P. R. China |
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| Abstract: | In this paper, the zeros of solutions of periodic second order linear differential equation $y'+Ay=0$, where $A(z)=B(e^z)$, $B(zeta)=g(zeta)+sum_{j=1}^pb_{-j}zeta^{-j}$, $g(zeta)$ is a transcendental entire function of lower order no more than $1/2$, and $p$ is an odd positive integer, are studied. It is shown that every non-trivial solution of above equation satisfies the exponent of convergence of zeros equals to infinity. |
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| Keywords: | periodic differential equation complex oscillation regular order of growth. |
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