一类一阶中立型时滞微分方程解的振动性

Oscillation of First-Order Neutral Delay Differential Equations

考虑一阶中立型时滞微分方程d/dt[x(t)+p(t)x(t-τ)]+f(t,x(t-σ))=0,其中p∈C([t0,∞),R),q∈C([t0,∞),R+),τ,σ∈R+,f(t,x)是定义在[t0,+∞)×R上的连续函数,讨论了上述方程的解的振动性,得出了该方程的一切解振动的充分条件。

Considering the first-order neutral delay differential equation d/dt[x（t）＋p（t）x（t-τ）]＋f（t,x（t-σ））=0,p∈C（[t0,∞）,R）,q∈C（[t0,∞）,R^＋）,τ,σ∈R^＋,and f（t,x）is a continuous function of [t0,＋∞）×RA sufficient condition is obtained guaranteeing every solution of the above equation.