华东师范大学学报(自然科学版) ›› 2007, Vol. 2007 ›› Issue (3): 39-48.

• 数学 统计学 • 上一篇    下一篇

一类二阶非线性脉冲微分方程的振动性（英）

张伟鹏, 毕平, 朱德明   

  1. 华东师范大学 数学系, 上海 200062
  • 收稿日期:2006-02-07 修回日期:2006-03-31 出版日期:2007-05-25 发布日期:2007-05-25
  • 通讯作者: 朱德明

Oscillations of Certain Second-Order Nonlinear Differential Equations with Impulses(English)

ZHANG Wei-peng, BI Ping, ZHU De-ming   

  1. Department of Mathematics, East China Normal University, Shanghai 200062, China
  • Received:2006-02-07 Revised:2006-03-31 Online:2007-05-25 Published:2007-05-25
  • Contact: ZHU De-ming

摘要： 利用Lakshmikantham等人建立的脉冲微分方程不等式研究了一类二阶脉冲常微分方程解的振动性, 获得了此类方程振动所应具备的充分条件. 同时改进了一些已知结果. 最后用一个具体例子说明了是否带有脉冲对微分方程的振动性有很大的影响.

关键词: 振动, 二阶微分方程, 脉冲, 振动, 二阶微分方程, 脉冲

Abstract: This paper considered the oscillatory behavior of solutions of a second-order impulsive ordinary differential equation by using impulsive differential inequalities established by Lakshmikantham et al. Sufficient conditions were obtained for all solutions of this type of equations to be oscillatory, illustrating that impulses play an important role in giving rise to the oscillation of equations. In particular, our work generalizes some known results. Finally, an example was presented to explain the key role of impulses in
generating oscillatory.

Key words: second-order differential equation, impulses, oscillation, second-order differential equation, impulses

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