Abstract
In this paper, we use a modification of Krasnoselskii's fixed point theorem introduced by Burton (see[8] Theorem 3) to obtain stability results of the zero solution of totally nonlinear neutral differential equations with functional delay
x'(t) = -a (t)h (x (t - tau (t)) + c(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) = G(t, 0, 0) = 0. The Caratheodory condition is used for the function G.