Center Manifold Theorem and Stability for Integral Equations with Infinite Delay
Copyright policy )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".
42 pages
- Okayama University of Science Japan
- Columbus State University United States
- Osaka Metropolitan University Japan
Mathematics - Functional Analysis, FOS: Mathematics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, 45M10, 34K20, Functional Analysis (math.FA)
Mathematics - Functional Analysis, FOS: Mathematics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, 45M10, 34K20, Functional Analysis (math.FA)
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