Boundary value problems with discontinuities in the spatial variable
type: Item
instance of: scholarly article
title: Boundary value problems with discontinuities in the spatial variable
zbMATH Open document ID: 0836.34025
author: Martin Šenkyřík
author: Ronald B. Guenther
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-04-22T00:00:00Z
review text: Under the assumption that \(f = f(t,x)\), \(x \in R^n\) is measurable, but not necessarily continuous, and using Filippov's theory, the problem (1) \(x' = f(t,x)\), \(x(0) = x(1)\) is reformulated as a differential inclusion and then the existence principles proved by \textit{A. Granas}, \textit{R. B. Guenther} and \textit{L. W. Lee} [C. R. Acad. Sci., Paris, Ser. I 307, No. 8, 391-396 (1988; Zbl 0652.34018)] are applied to prove the existence of a solution to (1).
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 34A60
zbMATH DE Number: 811588
zbMATH Keywords: periodic boundary value problem
zbMATH Keywords: Filippov's theory
zbMATH Keywords: differential inclusion
zbMATH Keywords: existence
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1236
OpenAlex ID: W2063189166
DOI: 10.1006/JMAA.1995.1236
description: scientific article; zbMATH DE number 811588