A STUDY OF THE STABILITY IN NEUTRAL NONLINEAR DIFFERENTIAL EQUATIONS WITH FUNCTIONAL DELAY VIA FIXED POINTS

Abstract

In this paper, we use a modification of Krasnoselskii's fixed point theorem introduced by Burton (see <cite>b0</cite> Theorem 3) to obtain stability results of the zero solution of the totally nonlinear neutral differential equations with functional delay

x′(t)=-a(t)h(x(t-τ(t)))+c(t)x′(t-τ(t))+G(t,x(t),x(t-τ(t))).

The stability of the zero solution of this eqution provided that h(0)=G(t,0,0)=0. The Caratheodory condition is used for the function G.