Solutions of Hammerstein integral equations via a variational principle
type: Item
instance of: scholarly article
title: Solutions of Hammerstein integral equations via a variational principle
zbMATH Open document ID: 1060.45006
author: Francesca Faraci
author: Vitaly Moroz
published in: Journal of Integral Equations and Applications
publication date: 2004-11-11T00:00:00Z
review text: The authors study solutions of the Hammerstein equation \[ u(x)= \int_\Omega k(x,y)f \bigl(y,u(y)\bigr)\,dy \] as critical points of the corresponding energy functional on a suitable Hilbert space. The main tool is a new variational principle of \textit{B. Ricceri} [J. Comput. Appl. Math. 113, No. 1--2, 401--410 (2000; Zbl 0946.49001)] which also applies to kernel functions \(k\) of changing sign. The abstract result is illustrated by means of an application to the polyharmonic equation \((-\Delta)^mu(x)= f(x,u(x))\).
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 49J22
Mathematics Subject Classification ID: 47J30
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 2114499
zbMATH Keywords: critical points
zbMATH Keywords: energy functional
zbMATH Keywords: Hilbert space
zbMATH Keywords: variational principle
zbMATH Keywords: polyharmonic equation
zbMATH Keywords: Hammerstein integral equations
reviewed by: Jürgen Appell
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/jiea/1181074983
OpenAlex ID: W2018287042
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DOI: 10.1216/JIEA/1181074983
description: scientific article; zbMATH DE number 2114499