时间测度链上一类具阻尼项的二阶动力方程的振动准则

上海交通大学学报（自然版） ›› 2012, Vol. 46 ›› Issue (09): 1529-1533.

时间测度链上一类具阻尼项的二阶动力方程的振动准则

杨甲山

(邵阳学院理学与信息科学系,湖南邵阳 422004)

收稿日期:2011-12-12 出版日期:2012-09-28 发布日期:2012-09-28
基金资助:
国家自然科学基金资助项目(11071222)，湖南省教育厅科研重点项目(09A082)

Oscillation Criteria for a Class of Second Order Dynamic Equations with Damping on Time Scales

YANG Jia-Shan

(Department of Science and Information, Shaoyang University, Shaoyang 422004, Hunan, China)

Received:2011-12-12 Online:2012-09-28 Published:2012-09-28

摘要/Abstract

摘要： 研究了时间测度链上一类具有阻尼项和非线性中立项的二阶非线性变时滞动力方程的振动性, 利用时间测度链上的理论, 结合广义的Riccati变换和一些不等式技巧,得到了该方程的几个新的振动准则. 这些准则不仅推广和改进了一些已知的结果，而且在时间测度链上统一了具有阻尼项的二阶非线性时滞微分方程和差分方程的振动性质.最后，举例说明文中给出的主要结论.

关键词: 阻尼项, 非线性中立项, 振动性, 时间测度链, 动力方程

Abstract: The oscillation for certain second-order nonlinear variable delay dynamic equations with damping term and nonlinear neutral term on time scales was discussed. By using the time scales theory and the generalized Riccati transformation and the inequality technique, some new oscillation criteria for the equations were established. The results extend and improve some known results, but also unify the oscillation of second-order nonlinear delay differential equations and second-order nonlinear delay difference equations with damping term. Some examples were given to illustrate the main results of this article.

Key words: oscillation, time scales, dynamic equations, damping term, nonlinear neutral term

中图分类号:

O 175.7

杨甲山. 时间测度链上一类具阻尼项的二阶动力方程的振动准则 [J]. 上海交通大学学报（自然版）, 2012, 46(09): 1529-1533.

YANG Jia-Shan. Oscillation Criteria for a Class of Second Order Dynamic Equations with Damping on Time Scales[J]. Journal of Shanghai Jiaotong University, 2012, 46(09): 1529-1533.

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