具有“积分小”系数的奇数阶中立型方程的振动性

Oscillations of Odd-Order Neutral Equations with an‘Integrally Small’ Coefficient

考虑中立型微分方程dndtn[x( t) -P( t) x( t-τ) ]+Q( t) x( t-σ) =0 , t≥ t0 ,( * )其中 n≥ 1 ,n为奇数 ,P( t) ,Q( t)∈ C( [t0 ,+∞ ) ,R+ ) τ>0 ,σ>0 .本文在不需要通常假设 ∫∞t0Q( s) ds=∞的条件下 ,获得了保证 ( * )的所有解振动的几个充分条件 ,并推广了文 [1 ]、[3]的相应结论 .

In this paper, we consider the n th order neutral differential equation d n d t n[x(t)-P(t)x(t-τ)]+Q(t)x(t-σ)=0(*) and obtain some sufficients condition on the oscillation of Eq(*) without the usually requirement that ∫ ∞ t 0 Q(s) d s=∞, which extend and improve results obtained in [1],[2],[3].