C1-smooth dependence on initial conditions and delay : spaces of initial histories of Sobolev type, and differentiability of translation in Lp

Nishiguchi Junya: C1-smooth dependence on initial conditions and delay : spaces of initial histories of Sobolev type, and differentiability of translation in Lp. (2019)

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Abstract

The objective of this paper is to clarify the relationship between the C 1 -smooth dependence of solutions to delay differential equations (DDEs) on initial histories (i.e., initial conditions) and delay parameters. For this purpose, we consider a class of DDEs which include a constant discrete delay. The problem of C 1 -smooth dependence is fundamental from the viewpoint of the theory of differential equations. However, the above mentioned relationship is not obvious because the corresponding functional differential equations have the less regularity with respect to the delay parameter. In this paper, we prove that the C 1 -smooth dependence on initial histories and delay holds by adopting spaces of initial histories of Sobolev type, where the differentiability of translation in L p plays an important role.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 91
ISSN: 1417-3875
Page Range: pp. 1-32
DOI: 10.14232/ejqtde.2019.1.91
Uncontrolled Keywords: Differenciálegyenlet - késleltetett
Additional Information: Bibliogr.: p. 30-32. ; összefoglalás angol nyelven
Date Deposited: 2020. Jan. 27. 13:47
Last Modified: 2021. Sep. 16. 10:42
URI: http://acta.bibl.u-szeged.hu/id/eprint/66358

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