Stability in neutral nonlinear differential equations with functional delay using Krasnoselskii-Burton's fixed-point

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))+b(t)G(x(t),x(t-τ(t))).

The stability of the zero solution of this equations provided that h(0)=G(0,0)=0.