时标上三阶时滞动力方程的振动性和渐近性

华东师范大学学报(自然科学版) ›› 2014, Vol. 2014 ›› Issue (3): 51-59.

时标上三阶时滞动力方程的振动性和渐近性

张晓建¹, 杨甲山²

1. 邵阳学院~~理学与信息科学系, 湖南~~邵阳 422004; 2. 梧州学院~~数理系, 广西~~梧州 543002

收稿日期:2013-06-01 修回日期:2013-09-01 出版日期:2014-05-25 发布日期:2014-07-25

Oscillation and asymptotic behaviors for third-order delay dynamic equations on time scales

ZHANG Xiao-jian¹, YANG Jia-shan²

1. Department of Science and Information, Shaoyang University, Shaoyang, Hunan 422004, China;
2. Department of Mathemedics and Physics, Wuzhou University, Wuzhou Guangxi 543002, China

Received:2013-06-01 Revised:2013-09-01 Online:2014-05-25 Published:2014-07-25

摘要/Abstract

摘要： 研究了时标上的一类非线性三阶中立型时滞动力方程的振动性,
运用\,Riccati\,变换技术和大量的不等式技巧,
获得了该方程的每一个解或者振动或者渐近于零的新充分条件,
推广和改进了一些已知结果, 并以具体例子来说明了本文的主要结论.

关键词: 振动性, 时滞动力方程, Riccati变换, 不等式技巧, 时标

Abstract: The oscillation for certain third-order nonlinear variable
delay dynamic equations on time scales was discussed in this
article. By using the generalized Riccati transformation and a lot
of inequality techniques, we established some new sufficient
conditions which ensure that every solution of the equations either
oscillates or converges to zero. The results extend and improve some
known results. Examples were given to illustrate the main results.

Key words: oscillation, delay dynamic equations, Riccati transformation, inequality techniques, time scales

中图分类号:

O157.5

张晓建, 杨甲山. 时标上三阶时滞动力方程的振动性和渐近性[J]. 华东师范大学学报(自然科学版), 2014, 2014(3): 51-59.

ZHANG Xiao-jian, YANG Jia-shan. Oscillation and asymptotic behaviors for third-order delay dynamic equations on time scales[J]. Journal of East China Normal University(Natural Sc, 2014, 2014(3): 51-59.

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