Stability of the zero solution of a family of functional-differential equations

We give some sufficient conditions under which the zero solution of the next functional-differential equation x'(t)-ax(t)+bx(tau(0)(t)) + Sigma(k)(j=1) c(j)(tau(j)(t)) + f(x(t),x(tau(k+1)(t)),.....,x(tau(k+1)(t))), where a, b, c(j) , j =(1,k) over bar are real numbers, f: Rl+1 -> R is a continuous function such that f(0,....,0) = 0, tau(j) is an element of C-2 [0, infinity 0, j = (0.k+1) over bar, is asymptotically stable. (c) 2014 Elsevier Inc. All rights reserved.