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浙江大学学报（理学版）
浙江大学学报（理学版）  2019, Vol. 46 Issue (4): 405-411    DOI: 10.3785/j.issn.1008-9497.2019.04.004
数学与计算机科学     
时间模上一类二阶泛函动态方程振荡的充分条件
李继猛1, 杨甲山2
1.邵阳学院 理学院, 湖南 邵阳 422004
2.梧州学院 大数据与软件工程学院, 广西 梧州 543002
Sufficient conditions of oscillation for certain second-order functional dynamic equations on time scales
LI Jimeng1, YANG Jiashan2
1.School of Science, Shaoyang University, Shaoyang 422004, Hunan Province, China
2.School of Data Science and Software Engineering, Wuzhou University, Wuzhou 543002, Guangxi Zhuang Autonomous Region, China
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摘要： 研究了一类时间模上二阶Emden-Fowler 型变时滞的中立型泛函动态方程{ a ( t ) φ( [ x ( t )+p ( t ) g ( x ( τ ( t ) ) ) ]Δ ) }Δ + q1 ( t ) f1 ( φ1 ( x ( δ1 ( t ) ) ) )+ q2 ( t ) f2 ( φ2 ( x ( δ2 ( t ) ) ) )= 0 的振荡性, 其中,φ( u )= |u|α - 1 u(α>0),φ1 ( u )= |u|β - 1 u(β>0),φ2 ( u )= |u|γ - 1 u(γ>0)。利用时间模上的有关理论和广义黎卡提变换技术, 并借助各种不等式, 得到了该方程振荡的一些新的充分条件, 推广并丰富了一些已有结果。最后，给出了一些有趣的实例以说明文中的结果。
关键词： 振荡性;  时间模;  泛函动态方程;  变时滞;  黎卡提变换    
Abstract: This paper is concerned with oscillatory behavior of the following second-order Emden-Fowler variable delay neutral functional dynamic equation { a ( t ) φ( [ x ( t )+ p ( t ) g ( x ( τ ( t ) ) ) ]Δ ) }Δ + q1 ( t ) f1 ( φ1 ( x ( δ1 ( t ) ) ) )+q2 ( t ) f2 ( φ2 ( x ( δ2 ( t ) ) ) )= 0 on a time scale T, where φ( u )= |u|α - 1 u(α >0), φ1 ( u )= |u|β - 1 u(β >0) and φ2 ( u )=|u|γ - 1 u(γ >0). By using the time scales theory and the Riccati transformation as well as the inequality technique, we establish some new sufficient conditions of oscillation for the equation. Our results deal with some cases not covered by the existing results in the literature. Finally, some interesting examples are given to illustrate the versatility of our results.
Key words: oscillation    time scales    functional dynamic equation    variable delay    Riccati transformation
收稿日期: 2018-07-01 出版日期: 2019-07-25
CLC:  O175.7  
基金资助: 湖南省自然科学基金资助项目(12JJ3008)；湖南省教育厅教学改革研究项目(2016jg671)；邵阳市科技计划项目(2016GX04).
作者简介: 李继猛(1964―),ORCID: https://orcid.org/0000-0002-9263-2878, 男,学士,副教授,主要从事微分方程理论与应用研究,E-mail:syxyljm@163.com.
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引用本文:

李继猛, 杨甲山. 时间模上一类二阶泛函动态方程振荡的充分条件[J]. 浙江大学学报（理学版）, 2019, 46(4): 405-411.

LI Jimeng, YANG Jiashan. Sufficient conditions of oscillation for certain second-order functional dynamic equations on time scales. Journal of Zhejiang University (Science Edition), 2019, 46(4): 405-411.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2019.04.004    或    https://www.zjujournals.com/sci/CN/Y2019/V46/I4/405

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