Topological transversality: Application to an integrodifferential equation
type: Item
instance of: scholarly article
title: Topological transversality: Application to an integrodifferential equation
zbMATH Open document ID: 0855.45006
author: A. Constantin
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-02-04T00:00:00Z
review text: Consider the following integrodifferential equation \[ x'(t) = F \left( t,x(t), \int^t_0 k \bigl[ t,s,x(s) \bigr] ds \right), \quad x(0) = 0, \tag{1} \] where \(k : \mathbb{R}^2_+ \times \mathbb{R} \to \mathbb{R}\), \(F : \mathbb{R}_+ \times \mathbb{R}^2 \to \mathbb{R}\) are continuous functions. The author studies the global existence of the solution of equation (1) under some suitable conditions on the functions \(k\) and \(F\) involved in (1). The main tools employed in the analysis are based on the applications of topological transversality arguments and an integral inequality recently established by the reviewer [J. Math. Anal. Appl. 189, No. 1, 128-144 (1995; Zbl 0824.26010)]. An application to water percolation phenomena is also given.
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 902477
zbMATH Keywords: integrodifferential equation
zbMATH Keywords: existence
zbMATH Keywords: topological transversality
zbMATH Keywords: integral inequality
zbMATH Keywords: water percolation phenomena
Wikidata QID: Q58870114
reviewed by: B. G. Pachpatte
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0057
OpenAlex ID: W2060442676
DOI: 10.1006/JMAA.1996.0057
description: scientific article; zbMATH DE number 902477