Center Manifold Theorem and Stability for Integral Equations with Infinite Delay

Abstract

The present paper deals with autonomous integral equations with infinite delay via dynamical system approach. Existence, local exponential attractivity, and other properties of center manifold are established by means of the variation-of-constants formula in the phase space that is obtained in our previous paper [22] (Funkcial. Ekvac. 55 (2012), 479-520). Furthermore, we prove a stability reduction principle by which the stability of an autonomous integral equation is implied by that of an ordinary differential equation which we call the "central equation".