Center manifold theorem and stability for integral equations with infinite delay

Matsunaga, H., Murakami, S., Nagabuchi, Y. and Van Minh, N.

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 [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".

Funkcial. Ekvac.

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