Uniform asymptotic stability for perturbed neutral delay differential equations ✩

One-dimensional perturbed neutral delay differential equations of the form (x(t ) − P(t,x(t − τ ))) = f (t,xt ) + g(t, xt ) are considered assuming that f satisfies −v(t)M(φ) f (t,φ) v(t)M(−φ), where M(φ) = max{0,maxs∈[−r,0] φ(s)}. A typical result is the following: if g(t,φ) w(t) φ and t+1 t w(s) ds →0, then the zero solution is uniformly asymptotically stable providing that the zero solution of the corresponding equation without perturbation (x(t ) − P(t,x(t − τ ))) = f (t,xt ) is uniformly asymptotically stable. Some known results associated with this equation are extended and improved.  2003 Elsevier Inc. All rights reserved