J4 ›› 2010, Vol. 07 ›› Issue (4): 612-616.

• 数学 • 上一篇    下一篇

具有分布偏差变元的二阶中立型时滞微分方程的振动性

李鹏松, 张雪艳   

  1. 东北电力大学 理学院, 吉林 吉林 132012
  • 收稿日期:2009-12-03 出版日期:2010-07-26 发布日期:2011-06-14
  • 通讯作者: 李鹏松 E-mail:pengsongli@yahoo.com.cn

Oscillation of SecondOrder Neutral Delay Differential Equationswith Distributed Deviating Argument

LI Pengsong, ZHANG Xueyan   

  1. College of Sciences, Northeast Dianli University, Jilin 132012, Jilin Province, China
  • Received:2009-12-03 Online:2010-07-26 Published:2011-06-14
  • Contact: LI Pengsong E-mail:pengsongli@yahoo.com.cn

摘要:

考虑如下具有分布偏差变元的二阶中立型时滞微分方程的振动性,利用广义的Riccati技巧和积分均值不等式, 并借助于一类新函数Φ(t,s,l)和类函数F, 放宽了对函数f的限制, 即当f不满足下述条件: 存在一个正数M, 使得(f(±uv))≥Mf(u)f(v), uv>0时, 建立了具有分布偏差变元的二阶中立型时滞微分方程新的振动准则, 数值实例验证了所得结果的正确性.

关键词: 振动; 中立型时滞微分方程; 分布偏差变元

Abstract:

The oscillation of second\|order neutral delay differential equations with distributed deviating argument, a class of new functions Φ(t,s,l) and the function cl
ass F, we relaxed the restriction on function f, namely, when f does not satisfy the following conditions: there exists M>0, such that (f(±uv))≥Mf(u)f(v), uv>0, and hence established some new oscillation criteria for secondorder neutral equations with distributed deviating argument. An example was given to illustrate the results.

Key words: oscillation, neutral delay differential equation, distributed deviating argument

中图分类号: 

  • O175.1