数学季刊 ›› 2013, Vol. 28 ›› Issue (2): 172-179.

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时间测度链上二阶非线性动力方程的振动性

  

  1. Department of Science and Information, Shaoyang University
  • 收稿日期:2011-07-07 出版日期:2013-06-30 发布日期:2023-02-28
  • 作者简介:YANG Jia-shan(1963-), male, native of Chengbu, Hunan, a professor of Shaoyang University,engages in differential and difference equation, dynamic system.
  • 基金资助:
    Supported by the Scientific Research Fund of Hunan Provincial Education Department(09A082)

Oscillation of Second-order Nonlinear Dynamic Equation on Time Scales

  1. Department of Science and Information, Shaoyang University
  • Received:2011-07-07 Online:2013-06-30 Published:2023-02-28
  • About author:YANG Jia-shan(1963-), male, native of Chengbu, Hunan, a professor of Shaoyang University,engages in differential and difference equation, dynamic system.
  • Supported by:
    Supported by the Scientific Research Fund of Hunan Provincial Education Department(09A082)

摘要:

The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many known results for second order dynamic equations. Some examples are given to illustrate the main results of this article.

关键词: time scales, dynamic equations, nonlinear neutral term, damping term, variable delay, Riccati transformation, oscillation

Abstract:

The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many known results for second order dynamic equations. Some examples are given to illustrate the main results of this article.

Key words: time scales, dynamic equations, nonlinear neutral term, damping term, variable delay, Riccati transformation, oscillation

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