Semiflows for differential equations with locally bounded delay on solution manifolds in the space \(C^1 ((-\infty, 0], {\mathbb R}^n)\)
type: Item
instance of: scholarly article
title: Semiflows for differential equations with locally bounded delay on solution manifolds in the space \(C^1 ((-\infty, 0], {\mathbb R}^n)\)
zbMATH Open document ID: 1371.34105
DOI: 10.12775/TMNA.2016.056
author: Hans-Otto Walther
published in: Topological Methods in Nonlinear Analysis
publication date: 2017-05-08T00:00:00Z
review text: In this big, interesting paper, with interesting results and nicely prepared, the author presents a construction of semiflow for autonomous differential equations with unbounded (locally bounded) delay. Some special cases of the problem, have been considered by the author in several other papers. Basic information about that are contained in the introduction. Also many ideas used in the paper (tangent cone, special Fréchet spaces, special Banach spaces, and some results used in the sequel) are presented with proofs in preliminaries. Special part of the paper is devoted for the properties of the ``semiflow on the solution manifold''. As it is stated by the author, the result presented in the paper, applies to autonomous differential equations with state-dependent delay which may be unbounded but which is locally bounded. ``The case of constant bounded delay, distributed or not, is included''. In my opinion, this paper requires from readers wide knowledge of mathematical ideas.
reviewed by: Stefan Czerwik
Mathematics Subject Classification ID: 34K05
Mathematics Subject Classification ID: 37L05
Mathematics Subject Classification ID: 34K30
zbMATH DE Number: 6712731
zbMATH Keywords: differential equation with delay
zbMATH Keywords: Fréchet space
zbMATH Keywords: unbounded delay
zbMATH Keywords: semiflow for differentialequation with delay
MaRDI profile type: Publication
full work available at URL: tmna.2016.056
OpenAlex ID: W2560312023
description: scientific article; zbMATH DE number 6712731