时间模上一类二阶阻尼Emden-Fowler型动态方程的振荡性

数学物理学报 ›› 2018, Vol. 38 ›› Issue (1): 134-155.

时间模上一类二阶阻尼Emden-Fowler型动态方程的振荡性

杨甲山^1,2, 李同兴³

1. 梧州学院信息与电子工程学院广西梧州 543002;
2. 梧州学院复杂系统仿真与智能计算实验室广西梧州 543002;
3. 临沂大学信息学院山东临沂 276005

收稿日期:2016-12-02 修回日期:2017-04-06 出版日期:2018-02-26 发布日期:2018-02-26
作者简介:杨甲山,syxyyjs@163.com;李同兴,litongx2007@163.com
基金资助:
国家自然科学基金（61503171，61403061，11447005）、广西教育厅科研基金（2013YB223）和硕士学位授予单位立项建设项目（桂学位[2013]4号）

Oscillation for a Class of Second-Order Damped Emden-Fowler Dynamic Equations on Time Scales

Yang Jiashan^1,2, Li Tongxing³

1. School of Information and Electronic Engineering, Wuzhou University, Guangxi Wuzhou 543002;
2. Laboratory of Complex System Simulation and Intelligent Computing, Wuzhou University, Guangxi Wuzhou 543002;
3. School of Informatics, Linyi University, Shandong Linyi 276005

Received:2016-12-02 Revised:2017-04-06 Online:2018-02-26 Published:2018-02-26
Supported by:
Supported by the NSFC (61503171, 61403061, 11447005), the Scientific Research Fund of Education Department of Guangxi Zhuang Autonomous Region (2013YB223) and the Master's Degree Awards Unit Project Construction Project (GUI Degree[2013]4)

摘要/Abstract

摘要： 该文研究了时间模上的一类具有阻尼项的二阶非线性中立型变时滞Emden-Fowler型动态方程的振荡性，利用时间模上的有关理论和广义的Riccati变换及不等式技巧，建立了该方程的6个新的振荡准则，这些准则推广和改进了一些已知的结果，在时间模上也统一了相应的二阶阻尼微分方程和差分方程的振荡性质.并给出了2个实例来说明该文的主要结论.

关键词: 振荡性, 中立型动态方程, 时间模, 阻尼项, 变时滞

Abstract: The oscillation for certain second-order nonlinear neutral variable delay Emden-Fowler dynamic equations with damping on time scales is discussed. By using the time scales theory and the generalized Riccati transformation and the inequality technique, we establish six new oscillation criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of second-order nonlinear damped Emden-Fowler differential equations and difference equations. Two examples are given to illustrate the main results of this article.

Key words: Oscillation, Neutral dynamic equations, Time scales, Damping term, Variable delay

中图分类号:

O175.7

杨甲山, 李同兴. 时间模上一类二阶阻尼Emden-Fowler型动态方程的振荡性[J]. 数学物理学报, 2018, 38(1): 134-155.

Yang Jiashan, Li Tongxing. Oscillation for a Class of Second-Order Damped Emden-Fowler Dynamic Equations on Time Scales[J]. Acta mathematica scientia,Series A, 2018, 38(1): 134-155.

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