Singularly perturbed functional-differential inclusions
type: Item
instance of: scholarly article
title: Singularly perturbed functional-differential inclusions
zbMATH Open document ID: 0834.34020
DOI: 10.1007/BF01038594
author: T. Donchev
author: Iordan Slavov
published in: Set-Valued Analysis
publication date: 1996-03-10T00:00:00Z
review text: The following singularly perturbed system of functional differential inclusions with state constraints is considered: \[ (x'(t), \varepsilon y'(t))\in F(t, x(t), y(t), x_t, y_t),\quad x(t)\in K_1,\;y(t)\in K_2, \] where \(K_1\), \(K_2\) are closed convex sets and \(x\in \mathbb{R}^n\), \(y\in \mathbb{R}^m\). Conditions on \(F\) are given which guarantee that the solution set \(Z(\varepsilon)\) of the above problem is either upper semicontinuous at \(\varepsilon= 0^+\) in \(C(I, \mathbb{R}^n)\times L^2(I, \mathbb{R}^m)\)-weak topology or it is lower semicontinuous with respect to \(C(I, \mathbb{R}^n)\times L^1(\mathbb{R}^m)\) topology.
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 49J24
Mathematics Subject Classification ID: 34K99
zbMATH DE Number: 815977
zbMATH Keywords: singularly perturbed system of functional differential inclusions with state constraints
reviewed by: Vlastimil Křivan
MaRDI profile type: Publication
cites work: Q4000472
cites work: Singular Perturbation in Mayer’s Problem for Linear Systems
cites work: Q4302119
cites work: Q5814121
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full work available at URL: https://doi.org/10.1007/bf01038594
OpenAlex ID: W2011323555
description: scientific article; zbMATH DE number 815977