Almost periodic solutions of differential equations in Banach spaces: Some new results and methods.
type: Item
instance of: scholarly article
title: Almost periodic solutions of differential equations in Banach spaces: Some new results and methods.
zbMATH Open document ID: 1035.34036
author: Toshiki Naito
author: Nguyen Van Minh
author: Jong Son Shin
published in: Vietnam Journal of Mathematics
publication date: 2003-07-15T00:00:00Z
review text: The article under review is a survey on recent results on almost-periodic solutions to differential and functional-differential equations of the form \(u'(t)=A(t)u(t)+f(t)\) and \(u'(t)=Au(t)+F(t)u_{t}+f(t)\) in Banach spaces. At the beginning, autonomous equations are investigated. The authors' approach, based on the spectral theory in the context of an evolution semigroup associated to the equation, allows the extension to the higher-order case. The main results are various criteria for the admissibility of function spaces for the equations under investigation. In the following sections, with similar techniques, the authors consider almost-periodic solutions to periodic equations (here, the conditions are stated in terms of spectral properties of the monodromy operators), and to functional-differential equations (in autonomous and periodic case). Several examples are provided.
Mathematics Subject Classification ID: 34C27
Mathematics Subject Classification ID: 37K30
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 1885681
zbMATH Keywords: almost-periodic solutions
zbMATH Keywords: evolution semigroups
zbMATH Keywords: spectral theory
zbMATH Keywords: monodromy operators
reviewed by: Gabriela Liţcanu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1885681