Filippov Lemma for certain second order differential inclusions
type: Item
instance of: scholarly article
title: Filippov Lemma for certain second order differential inclusions
zbMATH Open document ID: 1268.34044
author: Grzegorz Bartuzel
author: Andrzej Fryszkowski
published in: Central European Journal of Mathematics
publication date: 2013-02-18T00:00:00Z
review text: The paper is concerned with the following Cauchy problem for a second-order differential inclusion \[ x''\in A^2x+F(t,x),\quad x(0)=0,\quad x'(0)=0, \] where \(A\) is a non-degenerated \(n\times n\) real matrix and \(F:[0,1]\times {\mathbb R}\to {\mathcal P}({\mathbb R})\) is a set-valued map with closed values and Lipschitz in the second variable. An existence result for this problem is derived, starting from a given quasi solution. As usual for a Filippov-type existence theorem, the result provides an estimate between the quasi solution and the obtained solution.
reviewed by: Aurelian Cernea
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 26A24
Mathematics Subject Classification ID: 28A05
Mathematics Subject Classification ID: 28A15
zbMATH DE Number: 6137127
zbMATH Keywords: differential inclusion
zbMATH Keywords: differential operator
zbMATH Keywords: Lipschitz multifunction
zbMATH Keywords: Filippov lemma
MaRDI profile type: Publication
full work available at URL: s11533-012-0119-2
OpenAlex ID: W2088089467
Wikidata QID: Q124854891
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DOI: 10.2478/S11533-012-0119-2
description: scientific article; zbMATH DE number 6137127