童 玲，豆可可，林詩(shī)仲

（海南師范大學(xué) 數(shù)學(xué)與統(tǒng)計(jì)學(xué)院，海南 海口 571158）

具有正負(fù)系數(shù)的一階中立型時(shí)滯微分方程的振動(dòng)性

童 玲，豆可可，林詩(shī)仲

（海南師范大學(xué) 數(shù)學(xué)與統(tǒng)計(jì)學(xué)院，海南 ?？?571158）

建立了具有正負(fù)系數(shù)的一階中立型時(shí)滯微分方程的振動(dòng)性的一個(gè)新的振動(dòng)定理,它推廣了文獻(xiàn)中的若干結(jié)果.

振動(dòng)定理；一階中立型方程；正負(fù)系數(shù)

關(guān)于一階中立型時(shí)滯微分方程的振動(dòng)性，已有許多研究成果問世，例如文[1-9]，在本文中，筆者繼續(xù)對(duì)一階中立型時(shí)滯微分方程的振動(dòng)性進(jìn)行了研究，得到了一些新的振動(dòng)準(zhǔn)則.

本文考慮帶正負(fù)系數(shù)的一階中立型微分方程：

1 主要結(jié)果

2 例子

[1]Gyori I,Ladas,G.Oscillation Theory of Differential Equa?tions with Applications[M].Charendon Press,Oxford,1991.

[2]Ladas G,Sficas Y G.Oscillations of Neutral Delay Differ?ential Equations[J].Canad Math Bull,vol,1986,29(4):438-445.

[3]Copalsamy K,Zhang B G.Oscillation and Nonoscillation in First Order Neutral Differential Equations[J].J Math Anal Appl,1990,151(2):42-57.

[4]Lin S Z.Oscillation in First Order Neutral Differential Equations[J].Ann of Diff Eqa,2003,19(3):334-336.

[5]周勇,俞元洪.一階中立型時(shí)滯微分方程的振動(dòng)性[J].數(shù)學(xué)研究與評(píng)論,2001,21(3):86-88.

[6]Farrell K,Grove E A.,Ladas G.Neutral Delay Differential Equations with Positive and Negative Coefficients[J].Ap?pl Anal,1988,27(3):181-197.

[7]庾建設(shè).帶有正負(fù)系數(shù)的中立型微分方程[J].數(shù)學(xué)學(xué)報(bào),1991,34(2):517-523.

[8]Yu J S,Wang Z.Some Further Results on Oscillation of Neutral Differential Equations[J].Bull Aus Math Soc,1992,46(3):149-157.

[9]林詩(shī)仲,俞元洪.具有正負(fù)系數(shù)的一階中立型時(shí)滯微分方程的振動(dòng)性[J].數(shù)學(xué)研究,2005,38(3):277-280.

Oscillation of First Order Neutral Delay Differential Equations with Positive and Negative Coefficients

TONG Ling，DOU Keke，LIN Shizhong
（College of Mathematics，Hainan Normal University，Haikou571158，China）

In this paper,a new oscillation theorem for first order neutral delay differential equations with positive and negative coefficients is established,which generalizes and promotes several results in the literature.

First order neutral equation；Oscillation theorem；Positive and negative coefficients

O 175

A

1674-4942（2011）01-0015-03

2010-12-02

海南自然科學(xué)基金項(xiàng)目（110007）

畢和平