Bounded solutions of Carathéodory differential inclusions: a bound sets approach
type: Item
instance of: scholarly article
title: Bounded solutions of Carathéodory differential inclusions: a bound sets approach
zbMATH Open document ID: 1036.34011
DOI: 10.1155/S108533750321006X
author: Jan Andres
author: Luisa Malaguti
author: Valentina Taddei
published in: Abstract and Applied Analysis
publication date: 2003-06-18T00:00:00Z
full work available at URL: https://eudml.org/doc/50730
review text: Here, the authors prove the existence of bounded solutions to the following differential inclusion: \(x'\in F(t,x)\), \(t\in\mathbb{R},\) where \(F:\mathbb{R}\times \mathbb{R}^N\rightarrow\mathbb{R}^N\) is a Carathéodory multivalued map, with nonempty, compact and closed values. In order to do so, they first solve an appropriate Floquet boundary value problem using a bound sets technique, which relies on the construction of bounding functions which are either continuous or locally Lipschitz and also a modification of a continuation principle due to the first author, \textit{G. Gabor} and \textit{L. Górniewicz} [Trans. Am. Math. Soc. 351, 4861--4903 (1999; Zbl 0936.34023)]. Then, they apply a sequential approach to get a solution to the original problem. The paper is very clear, discusses in detail previous results in the area, contains two examples and concludes with suggestions for further research: generalization into \(L^2\) spaces and problems related to retarded functional-differential inclusions.
reviewed by: Nikos Yannakakis
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B40
zbMATH DE Number: 1929998
zbMATH Keywords: Bound sets technique
zbMATH Keywords: Floquet problems
zbMATH Keywords: bounding function
zbMATH Keywords: differential inclusion
zbMATH Keywords: Carathéodory multifunction
zbMATH Keywords: set-valued map
zbMATH Keywords: bounded solutions
zbMATH Keywords: upper semicontinuous multifunction
MaRDI profile type: Publication
OpenAlex ID: W1966496560
description: scientific article; zbMATH DE number 1929998