MR3379136 Hideaki MATSUNAGA, Satoru MURAKAMI, Yutaka NAGABUCHI and Nguyen VAN MINH Hideaki MATSUNAGA, Satoru MURAKAMI, Yutaka NAGABUCHI and Nguyen VAN MINH Center Manifold Theorem and Stability for Integral Equations with Infinite Delay Funkcialaj Ekvacioj. Serio Internacia 58 2015 87--134 http://fe.math.kobe-u.ac.jp/FE/FullPapers/58-1/58_87.pdf http://www.ams.org/mathscinet-getitem?mr=MR3379136 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”. Integral equations with infinite delay, Center manifolds, Stability properties, Phase space, A variation-of-constants formula. Primary: 45M10; Secondary: 34K20. 58-87 2015 Center Manifold Theorem and Stability for Integral Equations with Infinite Delay Hideaki MATSUNAGA, Satoru MURAKAMI, Yutaka NAGABUCHI and Nguyen VAN MINH Hideaki MATSUNAGA, Satoru MURAKAMI, Yutaka NAGABUCHI and Nguyen VAN MINH
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