An averaging method for singularly perturbed systems of semilinear differential inclusions with \(C_0\)-semigroups
type: Item
instance of: scholarly article
title: An averaging method for singularly perturbed systems of semilinear differential inclusions with \(C_0\)-semigroups
zbMATH Open document ID: 1034.34075
DOI: 10.1023/A:1025604317289
published in: Set-Valued Analysis
publication date: 2003-10-14T00:00:00Z
review text: A system of two semilinear differential inclusions in separable Banach spaces with infinitesimal generators of \(C_{0}\)-semigroups and multivalued uppersemicontinuous perturbations with compact convex values is considered. They are of high frequence with respect to time and periodic with a specifed period. Moreover, the perturbations are condensing in the state variables with respect to a suitable measure of noncompactness. For sufficiently small \(\varepsilon > 0\), the existence of periodic solutions and their behaviour as \(\varepsilon \rightarrow 0\) are studied. The main tool is the topological degree theory for uppersemicontinuous condensing vector fields. The work complements the previous results of the authors where is assumed that the infinitesmal generators of analytic semigroups have a compact inverse.
reviewed by: A. A. Tolstonogov
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 34D15
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 34E15
zbMATH DE Number: 1992540
zbMATH Keywords: differential inclusions
zbMATH Keywords: singularly perturbed systems
zbMATH Keywords: periodic solutions
zbMATH Keywords: averaging method
author: Mikhail Kamenskii
author: Paolo Nistri
MaRDI profile type: Publication
full work available at URL: a:1025604317289
OpenAlex ID: W3158163128
description: scientific article; zbMATH DE number 1992540