Study of the stability in nonlinear neutral differential equations with functional delay using Krasnoselskii-Burton's fixed-point

In this paper, we use a modification of Krasnoselskii's fixed point theorem introduced by Burton (2002) (see [6] Theorem 3) to obtain stability results of the zero solution of the totally nonlinear neutral differential equations with functional delay x'(t) = -alpha(t)h(x(t - tau(t))) + d/dt Q(t, x(t- tau(t))) = G(t, x(t), x(t- tau(t))). The stability of the zero solution of this equation provided that h(0) = Q(t, 0) = G(t, 0, 0) = 0. The Caratheodory condition is used for the functions Q and G. (C) 2014 Elsevier Inc. All rights reserved.