Bounded components of positive solutions of abstract fixed point equations: Mushrooms, loops and isolas
type: Item
instance of: scholarly article
title: Bounded components of positive solutions of abstract fixed point equations: Mushrooms, loops and isolas
zbMATH Open document ID: 1066.47063
author: Julián López-Gómez
author: Marcela Molina-Meyer
published in: Journal of Differential Equations
publication date: 2005-02-22T00:00:00Z
review text: Let \(U\) be an ordered Banach space whose positive cone is normal and has nonempty interior. This paper is devoted to the study of the nonlinear abstract equation \({\mathcal L}(\lambda)u+{\mathcal R}(\lambda,u)=0\) for \((\lambda ,u)\in \mathbb R\times U\), where \({\mathcal L}(\lambda)\) is a Fredholm operator of index \(0\) and \({\mathcal R}\in C(\mathbb R\times U;U)\) is compact on bounded sets and \(\lim_{u\rightarrow 0}{\mathcal R}(\lambda,u)/\| u\| =0\). The main result of the present paper concerns the bounded components of positive solutions emanating from \((\lambda,u)=(\lambda,0)\). The proofs are based on refined techniques from modern bifurcation theory.
reviewed by: Teodora-Liliana Rădulescu
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 47J15
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35B50
zbMATH DE Number: 2136120
zbMATH Keywords: positive solutions
zbMATH Keywords: compact solution components
zbMATH Keywords: nonlinear abstract equations
zbMATH Keywords: strong maximum principle
MaRDI profile type: Publication
full work available at URL: j.jde.2004.07.018
OpenAlex ID: W2073908216
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DOI: 10.1016/J.JDE.2004.07.018
description: scientific article; zbMATH DE number 2136120