Center Manifold Theorem and Stability for Integral Equations with   Infinite Delay
  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 a previous paper \cite{mur}. 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". 
Hideaki Matsunaga, Satoru Murakami, Yutaka Nagabuchi and Nguyen Van   Minh
math.DS math.FA