中立型时滞微分方程的渐近稳定性

Asymptotic Stability for Neutral Delay Differential Equations

考虑具有正负系数的中立型时滞微分方程ddt[x (t) - P(t) x(t-τ) ]+ Q(t) x(t-δ) - R(t) x(t-σ) =0 , t≥ t0 ,其中 P(t)∈ C([t0 ,∞ ) ,R) ,Q(t) ,R(t)∈ C([t0 ,∞ ) ,R+ ) ,τ,δ,σ∈ (0 ,∞ ) .获得了该方程零解一致稳定及渐近稳定的充分条件 。

Small Consider the neutral differential equation with positive and negative coefficients d d t[x(t)-P(t)x(t-τ)]+Q(t)x(t-δ)-R(t)x(t-σ)=0, \ t≥t\-0,where \$P(t)∈C([t\-0,∞),R),Q(t),R(t)∈C([t\-0,∞),R\++),τ,δ,σ∈(0,∞).\$ This paper obtain sufficient conditons for the zero solution of this equation to be uniformly stable as well as asymptotically stable. Which extend and improve the all known results in the literature.