一类无界时滞中立型微分方程的渐进稳定性

Asymptotic Stability for a Neutral Differential Equation with Unbounded Delays

考虑具有无界时滞的中立型微分方程d/(dt)[x(t)-P(t)x(αt)]+Q(t)x(βt)=0,t≥t0,P(t)∈C([t0,∞),R),Q(t)∈C([t0,∞),(0,∞)),0<α,β<1,当P(t)≠0时零解的一致稳定性和渐进稳定性,建立了该方程零解一致稳定及渐进稳定的充分条件.

This paper investigates the following neutral differential equation with unbounded delay d/（dt）[x（t）-P（t）x（αt）]＋Q（t）x（βt）=0,t≥t0 where P（t）∈C（[t0,∞）,R）,Q（t）∈C（[t0,∞）,（0,∞））,0〈α,β〈1,. Some sufficient conditions are established for the zero solution of this equation to be uniformly stable as well as asymptotically stable for P（t） ≠0.