时间模上一类二阶非线性动态方程振荡性的新准则

杨甲山; 黄劲

doi:10.3969/j.issn.1000-5641.2015.03.002

时间模上一类二阶非线性动态方程振荡性的新准则

doi: 10.3969/j.issn.1000-5641.2015.03.002

杨甲山^,,
黄劲

1.
梧州学院信息与电子工程学院, 广西梧州543002

基金项目:

广西教育厅科研基金项目(2013YB223);湖南省科技厅基金项目(2012FJ3107)

详细信息

作者简介:
杨甲山, 男, 教授,研究方向为微分差分方程及动力学方程. E-mail: syxyyjs@163.com.

通讯作者:
杨甲山, 男, 教授,研究方向为微分差分方程及动力学方程.

中图分类号: O175.7
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- 被引次数: 0
出版历程
- 收稿日期: 2014-08-26
- 刊出日期: 2015-05-25

New criteria for oscillation of certain second-order nonlinear dynamic equations on time scales

YANG Jia-shan^,,
HUANG Jin

摘要

摘要: 为了进一步发展和完善时间模上动态方程的振荡性理论,研究了下面的时间模\,\textbf{T}\,上一类二阶中立型变时滞非线性的动态方程\,$[A(t)\phi([x(t)+B(t)g(x(\tau (t)))]^\Delta )]^\Delta +f(t,x(\delta(t)))=0$\,的振荡性, 其中\,$\phi (u)=\vert u\vert ^{\lambda-1}u(\lambda0$\,为任意常数). 利用时间模上的微积分理论和不等式技巧,得到了该方程振荡的一些新准则. 最后, 举例说明了本文定理的应用.
- 振荡性 /
- 时间模 /
- 中立型动态方程 /
- 变时滞 /
- 非线性中立项
Abstract: In order to develop and improve the theory about oscillation of dynamic equations on time scales, this paper is concerned with the oscillatory behavior of the following second-order neutral variable delay nonlinear dynamic equation $[A(t)\phi ([x(t)+B(t)g(x(\tau (t)))]^\Delta)]^\Delta +f(t,x(\delta(t)))=0 on a time scale \textbf{T}, where phi (u)=\vert u\vert^{\lambda -1}u$, $\lambda $ is an arbitrary positive constant. By using the calculus theory on time scales and the inequality technique, we establish some new oscillation criteria for the equation. Finally, example is presented to illustrate the effects of our theorems.
- oscillationtime scalesneutral dynamic equationsvariable delaynonlinear neutral term /

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参考文献(1)

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