Homotopy and bounded solutions of ordinary differential equations
type: Item
instance of: scholarly article
title: Homotopy and bounded solutions of ordinary differential equations
zbMATH Open document ID: 0794.34027
published in: Journal of Differential Equations
publication date: 1994-04-19T00:00:00Z
review text: Global existence theorems are proved for nonautonomous equations of the type (1) \(x'(t)= f(x(t))+ g(x(t),t)\), \(t\in\mathbb{R}\) under various hypotheses on the functions \(f\), \(g\). A continuation theorem is proved and applied to obtain the existence of a globally bounded solution \(x(t)\) of (1) in \(\mathbb{R}\). The method is based on Conley index theory for compact isolated invariant sets in flows associated with (1).
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 553872
zbMATH Keywords: global existence
zbMATH Keywords: continuation theorem
zbMATH Keywords: globally bounded solution
zbMATH Keywords: Conley index
author: James Robert jun. Ward
reviewed by: Charles A. Swanson
MaRDI profile type: Publication
full work available at URL: jdeq.1994.1021
OpenAlex ID: W2030446134
DOI: 10.1006/JDEQ.1994.1021
description: scientific article; zbMATH DE number 553872