| 时间模上高阶动力学方程的有界解的振动性 |
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| 引用本文： | 周学勇,李连兵,师向云.时间模上高阶动力学方程的有界解的振动性[J].信阳师范学院学报(自然科学版),2006,19(3):258-260,270. |
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| 作者姓名： | 周学勇 李连兵 师向云 |
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| 作者单位： | 信阳师范学院,数学与信息科学学院,河南,信阳,464000 |
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| 基金项目： | YouthFoundationofXinyangNormalUniversity(20060201) |
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| 摘 要： | 给出了时间模上的高阶动力学方程xΔ(n)(t) f(t,x(t))=0的有界解振动或趋向于0的充分必要条件,即:当n是偶数时解是振动的;当n是奇数时解要么是振动的,要么是趋向于0.该文所用方法为研究时间模上高阶动力学方程的振动性提供了新的方法,且所得结果也统一和推广了连续和离散的动力学系统的理论.
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| 关 键 词： | 振动性 渐近性 时间模 动力学方程 |
| 文章编号： | 1003-0972（2006）03-0258-03 |
| 收稿时间： | 2005-10-09 |
| 修稿时间： | 2005-10-09 |
On the Oscillatory Behavior of Bounded Solutions of Higher Order Dynamic Equation on Time Scales |
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| ZHOU Xue-yong,LI Lian-bing,SHI Xiang-yun.On the Oscillatory Behavior of Bounded Solutions of Higher Order Dynamic Equation on Time Scales[J].Journal of Xinyang Teachers College(Natural Science Edition),2006,19(3):258-260,270. |
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| Authors: | ZHOU Xue-yong LI Lian-bing SHI Xiang-yun |
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| Institution: | College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, China |
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| Abstract: | It is given sufficient and necessary conditions of the bounded solutions ofxΔ(n)(t)+f(t,x(t))=0,which are oscillatory for n even and are oscillatory or tend monotonically to zero as t→∞ for n odd.We offer a new method on studying the oscillation of higher order dynamic equation on time scales.And the results generalize the theory of continuous and discrete dynamic equation. |
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| Keywords: | oscillation asymptotic time scales dynamic equation |
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