Massera problem for non-autonomous retarded differential equations
type: Item
instance of: scholarly article
title: Massera problem for non-autonomous retarded differential equations
zbMATH Open document ID: 1280.34076
author: Mohamed Zitane
author: Ch. Bensouda
published in: Journal of Mathematical Analysis and Applications
publication date: 2013-04-22T00:00:00Z
review text: The existence of an \(\omega\)-periodic mild solution of a reaction-diffusion equation is proven as an application of an abstract result. Starting from an existence result of a fixed point for a multivalued map defined on a nonempty convex set in a Banach space, conditions are established which ensure the existence of an \(\omega\)-periodic mild solution of a nonhomogeneous linear equation. Using the Poincaré map, the authors prove the equivalence between the existence of a bounded mild solution and the existence of an \(\omega\)-periodic mild solution of the considered problem.
reviewed by: Andrei Horvat-Marc
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K12
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6156138
zbMATH Keywords: evolution family
zbMATH Keywords: mild solution
zbMATH Keywords: periodic solutions
zbMATH Keywords: fixed point theorem
zbMATH Keywords: multivalued map
zbMATH Keywords: Poincaré map
MaRDI profile type: Publication
full work available at URL: j.jmaa.2013.01.046
OpenAlex ID: W2069512241
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DOI: 10.1016/J.JMAA.2013.01.046
description: scientific article; zbMATH DE number 6156138