Applications of linking to Hammerstein integral equations
type: Item
instance of: scholarly article
title: Applications of linking to Hammerstein integral equations
zbMATH Open document ID: 1231.45014
author: Donal O'Regan
published in: Applied Mathematics and Computation
publication date: 2011-03-08T00:00:00Z
review text: The critical point theory is used to establish existence results concerning Hammerstein integral equations of the form \[ u(x) = \lambda \int_{\Omega} k(x,y) u (y) dy - \int_{\Omega}k(x,y) f (y,u(y)) dy, \quad x \in \Omega \] where \(\lambda>0\) is a constant and \(\Omega\) is a closed bounded set in \(\mathbb R^n\). The main results are obtained using the concept of linking (both homotopical and (co)homological). The kernel \(k:\Omega\times\Omega\to\mathbb R\) satisfies the following conditions: (i) \(k\in C(\Omega\times\Omega,\mathbb R)\), (ii) \(k(x,y)=k(y,x)\) for \(x,y\in\Omega\), (iii) \(\int_{\Omega\times\Omega}k(x,y)u(x)u(y)dxdy\geq0\), for all \(u\in L^2(\Omega)\).
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 5862464
zbMATH Keywords: Hammerstein integral equation
zbMATH Keywords: existence problem
zbMATH Keywords: critical point theory
zbMATH Keywords: linking
MaRDI profile type: Publication
full work available at URL: j.amc.2010.11.051
OpenAlex ID: W1984722678
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DOI: 10.1016/J.AMC.2010.11.051
description: scientific article; zbMATH DE number 5862464