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 delayx′t=-athxt-τt+ddtQt,xt-τt+Gt,xt,xt-τt.The stability of the zero solution of this equation provided that h(0)=Q(t,0)=G(t,0,0)=0h0=Qt,0=Gt,0,0=0. The Caratheodory condition is used for the functions Q and G.