中立型方程d/(dt)[x(t)+px(t-τ)-rx(t-ρ)]+qx(t-s)-hx(t-v)=0的振动性

On the Oscillations of the Neutral Equations d dt [x(t)+px(t-τ)-rx(t-ρ)]+qx(t-s)-hx(t-v)=0

本文研究了既具正系数又具负系数的一阶中立型微分方程ｄｄｔ［ｘ（ｔ）＋ｐｘ（ｔ－τ）－ｒｘ（ｔ－ρ）］＋ｑｘ（ｔ－ｓ）－ｈｘ（ｔ－ｖ）＝０其中ｐ，ｒ，τ，ρ，ｑ，ｈ，ｓ，ｖ都是正的常数，建立了一切解振动的带有若干个可调参数的一个充要条件和一系列充分性判据及某种形式的一个充要条件．有些充要条件和充分性判据包含或改进了前人的相应结果．

In this paper, we study the oscillations of first order neutral delay differential equations with both positive and negative coefficients of the form d dt [x(t)+px(t-τ)-rx(t-ρ)]+qx(t-s)-hx(t-v)=0where the coefficients and the delays are positive constants. We obtain a necessary and sufficient condition with several changeable parameters and a series of sufficient criteria for the equations and a necessary and sufficient condition in a certain from for the equation to be oscillatory. Some necessary and sufficient conditions and sufficient criteria contain and further improve some corresponding results of the former authors.