Generalized differential equations: differentiability of solutions with respect to initial conditions and parameters
type: Item
instance of: scholarly article
title: Generalized differential equations: differentiability of solutions with respect to initial conditions and parameters
zbMATH Open document ID: 1279.34013
author: Antonín Slavík
published in: Journal of Mathematical Analysis and Applications
publication date: 2013-04-22T00:00:00Z
review text: The author proves the differentiability of solutions of generalized differential equations with respect to initial conditions and parameters. The term generalized differential equation means a nonlinear integral equation involving the Kurzweil integral. The present results extend the work by \textit{J. Kurzweil} [Czech. Math. J. 7(82), 418--449 (1957; Zbl 0090.30002)] and \textit{Š Schwabik} [Generalized ordinary differential equations. Singapore: World Scientific (1992; Zbl 0781.34003)]. They also unify the differentiability properties of solutions for differential equations with impulses or for dynamic equations on time scales. The proof of the main result is based on the arguments of \textit{R. Hilscher, V. Zeidan} and \textit{W. Kratz} [``Differentiation of solutions of dynamic equations on time scales with respect to parameters'', Adv. Dyn. Syst. Appl. 4, No. 1, 35--54 (2009), \url{http://campus.mst.edu/adsa}].
reviewed by: Roman Šimon Hilscher
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34N05
Mathematics Subject Classification ID: 34A37
zbMATH DE Number: 6156121
zbMATH Keywords: generalized ordinary differential equations
zbMATH Keywords: differentiability of solutions
zbMATH Keywords: Kurzweil integral
zbMATH Keywords: differential equations with impulses
zbMATH Keywords: dynamic equations on time scales
MaRDI profile type: Publication
full work available at URL: j.jmaa.2013.01.027
OpenAlex ID: W2024986253
Wikidata QID: Q56502421
DOI: 10.1016/J.JMAA.2013.01.027
description: scientific article; zbMATH DE number 6156121