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J4 ›› 2013, Vol. 48 ›› Issue (4): 85-90.

• 论文 • 上一篇    下一篇

含分布时滞与阻尼项的三阶非线性微分方程的Philos型振动

高正晖,罗李平   

  1. 衡阳师范学院数学与计算科学系, 湖南 衡阳 421008
  • 收稿日期:2012-05-04 出版日期:2013-04-20 发布日期:2013-04-16
  • 作者简介:高正晖(1959- ), 男, 副教授, 研究方向为微分方程. Email:gaozh828@163.com
  • 基金资助:

    湖南省重点学科建设项目“运筹学与控制论”资助

Philos-type oscillation criteria for third-order nonlinear functional differential equations with distributed delays and damped terms

GAO Zheng-hui, LUO Li-ping   

  1. Department of Mathematics and Computational Science, Hengyang Normal University,
    Hengyang 421008, Hunan, China
  • Received:2012-05-04 Online:2013-04-20 Published:2013-04-16

摘要:

 研究了一类含分布时滞与阻尼项的三阶非线性泛函微分方程
[r(t)x″(t)]′+p(t)x′(t)+∫baq(t,ξ)f(x(σ(t,ξ)))dξ=0,
利用广义Riccati变换和H函数技巧, 建立了保证此方程一切解Philos型振动或者收敛到零的若干新的充分条件。

关键词: 三阶泛函微分方程; 非线性; 分布时滞; 阻尼项; Philos型振动

Abstract:

The oscillation of third-order nonlinear neutral functional differential equations with distributed delays and damped terms is studied. By using a generalized Riccati transformation and H-functions technique, some new sufficient conditions which insure that any solution of this equation Philos-type oscillation or converges to zero are established.

Key words: third-order functional differential equation; nonlinear; distributed delays; damped terms; Philos-type oscillation

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