Uniform asymptotic stability for perturbed neutral delay differential equations (Q1433363)

The authors consider a one-dimensional perturbed neutral delay differential equation of the form \[ \frac{d(x(t)-P(t,x(t-\tau )))}{dt}=f(t,x_{t})+g(t,x_{t}), \] where \(\tau >0\) is a constant, \(P(t,0)=f(t,0)=g(t,0)\equiv 0\) and \(f,g :\mathbb{R}^{+}\times C(H)\rightarrow \mathbb{R},\) \(P:\mathbb{R}^{+}\times \mathbb{R}\rightarrow \mathbb{R}\) are continuous. Two sufficient conditions for the zero solution to be uniformly asymptotically stable are presented.