Existence of solutions and bifurcation points to Hammerstein equations with essentially bounded kernel
type: Item
instance of: scholarly article
title: Existence of solutions and bifurcation points to Hammerstein equations with essentially bounded kernel
zbMATH Open document ID: 1067.45001
author: Giovanni Anello
author: Giuseppe Cordaro
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-11-23T00:00:00Z
review text: This paper deals with an existence theorem of solutions and of bifurcation points for the Hammerstein integral equation \[ u(x)=\lambda\int_{\Omega}k(x,y)f(y,u(y))dy, \] where \(\lambda\in \mathbb R\), \(\Omega\) is a Lebesgue measurable subset of \(\mathbb R^{n}, \;k\in L^{\infty}(\Omega\times\Omega)\) and \(f:\Omega\times \mathbb R\to \mathbb R\) is a Carathéodory function. The proofs rely on the Tychonoff fixed point theorem.
reviewed by: Mouffak Benchohra
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 2117742
zbMATH Keywords: Hammerstein equations
zbMATH Keywords: bifurcation point
zbMATH Keywords: fixed point
zbMATH Keywords: essentially bounded kernel
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.05.015
OpenAlex ID: W1964365781
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DOI: 10.1016/J.JMAA.2004.05.015
description: scientific article; zbMATH DE number 2117742