临界状态下一阶中立型时滞微分方程的振动性

来源期刊：中南大学学报(自然科学版)1999年第6期

论文作者：唐先华 刘碧玉

文章页码：642 - 644

关键词：中立型;时滞微分方程;振动;临界状态

Key words：neutral; delay differential equation; oscillation; critical state

摘    要：证明了一阶中立型时滞微分方程[x(t)-p(t)x(t-τ)]′+Q(t)x(t-σ)=0所有解振动,如果limp(t)=1且liminf Q(s)ds>0,其中P(t),Q(t)ε C([t₀,∞),τ,σ(0,∞).

Abstract: It is proved that all solutions of the first order neutral delay differential equations [x(t)-p(t)x(t-τ)]′+Q(t)x(t-σ)=0 oscillate provided that lin P(t)=1 and liminf Q(s)ds>0,where P(t),Q(t)ε C([t₀,∞),R⁺),τ,σ(0,∞).