中山大学学报自然科学版 ›› 2012, Vol. 51 ›› Issue (1): 30-34.

• 研究论文 • 上一篇    下一篇

具正负系数和阻尼项的高阶微分方程的振动定理

杨甲山   

  1. (邵阳学院理学与信息科学系, 湖南 邵阳 422004)
  • 收稿日期:2011-04-10 修回日期:1900-01-01 出版日期:2012-01-25 发布日期:2012-01-25

Oscillation Theorems of Higher Order Differential Equations with Positive and Negative Coefficients and Damping Term

YANG Jiashan

  

  1. (Department of Science and Information, Shaoyang University, Shaoyang 422004, China)
  • Received:2011-04-10 Revised:1900-01-01 Online:2012-01-25 Published:2012-01-25

摘要: 研究了一类同时具有正负系数和阻尼项的高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,获得了该类方程振动的判别准则,这些准则改善了对方程的条件限制,所得结论推广并改进了现有文献中的一系列结果,并给出了具体例子用以说明主要结论。

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

Abstract: The oscillation for a class of higher order nonlinear variable delay functional differential equation with positive and negative coefficients and damping term is discussed. By introducing parameter function and the generalized Riccati transformation, some criteria for the oscillation of the equation are proposed. These criteria improve the restriction of the conditions for the equation. And these results improve and generalize some corresponding known results. Some examples are given to illustrate the main results.

Key words: positive and negative coefficient, functional differential equation, variable delay, damping term, Riccati transformation, oscillation

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