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)=-a(t)h(x(t-τ(t)))+d/dtQ(t,x(t-τ(t)))+G(t,x(t-τ(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. [ABSTRACT FROM AUTHOR]