华东师范大学学报(自然科学版) ›› 2005, Vol. 2005 ›› Issue (5/6): 79-84,1.

• 数学 统计学 • 上一篇    下一篇

一类二阶时滞微分方程解的振荡性、有界性和单调性

张晓霞   

  1. 上饶师范学院, 江西 上饶 334001
  • 收稿日期:2003-12-15 修回日期:2004-02-25 出版日期:2005-12-31 发布日期:2005-12-31
  • 通讯作者: 张晓霞

Oscillatory, Bounded and Monotone Properties of A kind of Delay Second-order Differential Equations(Chinese)

ZHANG Xiao-xia   

  1. Shangrao Normal College, Shangrao, JiangXi Province 334001, China
  • Received:2003-12-15 Revised:2004-02-25 Online:2005-12-31 Published:2005-12-31
  • Contact: ZHANG Xiao-xia

摘要： 研究二阶时滞拟线性微分方程(p(t -τ )(y'(t - τ))α)' = q(t)yβ(t) + r(t)(t ≥t0),解的振荡性, 有界性和单调性, 获得了一些新结果. 其中, t0和τ都是非负实数; 当t ≥ t0,时, p(t)是连续的正实函数, r(t)是连续的实函数,q(t)是非负的连续的实函数, 且q(t)不恒等于0; α和β都是正奇整数的商数.所得到的结果是文献[4]的推广.

关键词: 时滞拟线性微分方程解, 振荡性, 有界性, 单调性, 时滞拟线性微分方程解, 振荡性, 有界性, 单调性

Abstract:

Some new results are obtained for the oscillatory, bounded and monotone properties of solutions of forced second-order quaslinear equation (p(t -τ )(y'(t - τ))α)' = q(t)yβ(t) + r(t),t ≥ t0, where,t0 and τ are all nonnegative real numbers, when t ≥ t0,p(t) is a postive real continuous function,r(t) is a real continuous function, q(t) is a nonnegative real continuous function and q(t)is not zero function , α and β are quotients of odd positive integers.

Key words: monotone, bounded, oscillatory, solutions, quaslinear differential equation, monotone, bounded, oscillatory, solutions

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