华东师范大学学报(自然科学版) ›› 2011, Vol. 2011 ›› Issue (2): 10-16，3.

• 应用数学与基础数学 • 上一篇    下一篇

具有正负系数的二阶中立型方程的振动性定理

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:2010-04-01 修回日期:2010-07-01 出版日期:2011-03-25 发布日期:2011-03-25
  • 通讯作者: 杨甲山

Oscillation theorems of second order neutral differential equations with positive and negative coefficients

YANG Jia-shan   

  1. Department of Science and Information, Shaoyang University，Shaoyang Hunan 422004, China
  • Received:2010-04-01 Revised:2010-07-01 Online:2011-03-25 Published:2011-03-25
  • Contact: YANG Jia-shan

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摘要： 利用Banach空间的不动点原理, 通过引入参数函数和Riccati变换, 获得了该类方程存在非振动解的新的准则, 并同时得到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.

关键词: 正负系数, 中立型泛函数微分方程, 非线性, 振动和非振动, Riccati变换, 正负系数, 中立型泛函数微分方程, 非线性, 振动和非振动, Riccati变换

Abstract: Using the fixed point theorem in Banach space, and by introducing parameter function and the generalized Riccati transformation, a new nonoscillation criteria for the equation was obtained. In addition, a sufficient condition for oscillation of the equation was proposed. These criteria can improve the restriction of the conditions for the equation. Some existed results in the literatures have been further improved and extended.

Key words: neutral functional differential equation, nonlinear, oscillation and nonoscillation, Riccati transformation, positive and negative coefficient, neutral functional differential equation, nonlinear, oscillation and nonoscillation, Riccati transformation

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