On the solution manifold of a differential equation with a delay which has a zero

For a differential equation with a state-dependent delay we show that the associated solution manifold Xf of codimension 1 in the space C 1 ([−r, 0], R) is an almost graph over a hyperplane, which implies that Xf is diffeomorphic to the hyperplane. For the case considered previous results only provi...

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Bibliographic Details
Main Author: Walther Hans-Otto
Format: Serial
Published: 2022
Series:Electronic journal of qualitative theory of differential equations
Kulcsszavak:Differenciálegyenlet
Subjects:
doi:10.14232/ejqtde.2022.1.31

Online Access:http://acta.bibl.u-szeged.hu/76532
Description
Summary:For a differential equation with a state-dependent delay we show that the associated solution manifold Xf of codimension 1 in the space C 1 ([−r, 0], R) is an almost graph over a hyperplane, which implies that Xf is diffeomorphic to the hyperplane. For the case considered previous results only provide a covering by 2 almost graphs.
Physical Description:10
ISSN:1417-3875