Homoclinic solutions to an integral equation: Existence and stability
type: Item
instance of: scholarly article
title: Homoclinic solutions to an integral equation: Existence and stability
zbMATH Open document ID: 0934.45005
author: Xiaofeng Ren
author: Adam J. J. Chmaj
published in: Journal of Differential Equations
publication date: 2000-04-11T00:00:00Z
review text: The authors study (stationary) evolution equation in the form of the following nonlinear convolution type integral equation \[ (J\ast u)(x)- u(x)-f[u(x)]=0,\tag{1} \] with the condition \(u(\pm \infty)=0.\) It is assumed, that \(J(z)\geq 0\), \(\int J(z) dz =1\) and \(f\) is bistable. They construct homoclinic (even) solutions to the equation (1).
Mathematics Subject Classification ID: 45G05
Mathematics Subject Classification ID: 45M10
zbMATH DE Number: 1309590
zbMATH Keywords: homoclinic solutions
zbMATH Keywords: evolution equations
zbMATH Keywords: stability
zbMATH Keywords: nonlinear convolution type integral equation
reviewed by: N. Karapetiants
MaRDI profile type: Publication
full work available at URL: jdeq.1998.3571
OpenAlex ID: W1988711944
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DOI: 10.1006/JDEQ.1998.3571
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description: scientific article; zbMATH DE number 1309590