Stability results by Krasnoselskii-Burton theorem in nonlinear neutral integro-differential equation with variable delay

Stability in neutral integro-differential equations

Abstract

In this paper we consider the nonlinear neutral integro-differential equation with variable delay  x′(t)=-∫_{t-Ï„(t)}^{t}a(t,s)g(x(s))ds+(d/(dt))Q(t,x(t-Ï„(t)))+G(t,x(t),x(t-Ï„(t))), and give some new conditions for the boundedness and stability by means of Krasnoselskii-Burton's fixed point theory. The Caratheodory condition is used for the functions Q and G. The results obtained here extend and improve some earlier publications.