Nonlinear alternatives of Schauder and Krasnosel'skij types with applications to Hammerstein integral equations in \(L^1\) spaces
type: Item
instance of: scholarly article
title: Nonlinear alternatives of Schauder and Krasnosel'skij types with applications to Hammerstein integral equations in \(L^1\) spaces
zbMATH Open document ID: 1208.47044
author: Zahira Sahnoun
author: Smail Djebali
published in: Journal of Differential Equations
publication date: 2010-10-22T00:00:00Z
review text: In this interesting paper, by using the De Blasi measure of weak noncompactness, the authors establish some new variants of nonlinear alternatives of Leray-Schauder and Krasnosel'skij type involving the weak topology of Banach spaces. In addition, the authors apply their abstract results to a nonlinear Hammerstein integral equation in \(L^{1}\) spaces. The main results of this paper complement some recent ones due to \textit{K.\,Latrach, M.\,A.\thinspace Taoudi} and \textit{A.\,Zeghal} [J.~Differential Equations 221, 256--2710 (2006; Zbl 1091.47046)] and \textit{K.\,Latrach} and \textit{M.\,A.\thinspace Taoudi} [Nonlinear Anal.\ 66, 2325--2333 (2007; Zbl 1128.45006)].
Mathematics Subject Classification ID: 47H08
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5804424
zbMATH Keywords: weak topology
zbMATH Keywords: measure of weak noncompactness
zbMATH Keywords: fixed point theorem
zbMATH Keywords: nonlinear alternative
zbMATH Keywords: Hammerstein equation
MaRDI profile type: Publication
full work available at URL: j.jde.2010.07.013
OpenAlex ID: W1997792103
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DOI: 10.1016/J.JDE.2010.07.013
description: scientific article; zbMATH DE number 5804424