华东师范大学学报(自然科学版) ›› 2014, Vol. 2014 ›› Issue (6): 25-34.doi: 10.3969/j.issn.1000-5641.2014.06.005

• 应用数学与基础数学 • 上一篇    下一篇

具正负系数和阻尼项的高阶泛函微分方程的振动性

杨甲山   

  1. 梧州学院数理系, 广西,梧州 543002
  • 出版日期:2014-11-25 发布日期:2015-02-07
  • 通讯作者: 杨甲山, 男,教授, 研究方向为微分差分方程及动力方程. E-mail:syxyyjs@163.com
  • 基金资助:

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

Oscillation of higher order functional differential equations with positive and negative coefficients and damping term

 YANG  Jia-Shan   

  1. Department of Mathematics and Physics, Wuzhou University, Wuzhou Guangxi 543002, China
  • Online:2014-11-25 Published:2015-02-07

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摘要： 研究了一类同时具有正负系数和非线性中立项及阻尼项的偶数阶非线性变时滞泛函微分方程的振动性, 通过引入参数函数和Riccati变换，结合Holder不等式 及一些分析技巧,获得了该类方程振动的一些新的判别准则, 所得结论推广并改进了现有文献中的一些结果. 给出了具体例子, 用以说明文中的主要结论.

关键词: 振动性, 正负系数, 阻尼项, 泛函微分方程, Riccati变换

Abstract: The oscillation for a class of even order nonlinear variable delay damped functional differential equation with positive and negative coefficients and nonlinear neutral term was discussed. By introducing parameter function and the generalized Riccati transformation, using H¨older inequality and some necessary analytic techniques, some new criteria for the oscillation of the equation were proposed. These criteria improve and generalize some known results. Examples were given to illustrate the main results.

Key words: oscillation, positive and negative coefficient, damped term, functional differential equation, Riccati transformation

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