Topological identification of multiple solutions to parametrized nonlinear equations
type: Item
instance of: scholarly article
title: Topological identification of multiple solutions to parametrized nonlinear equations
zbMATH Open document ID: 0615.47042
author: Robert F. Brown
published in: Pacific Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Let L:E\(\to F\) be an isomorphism of Banach spaces, let \(H:E\times R^ n\to F\) be a completely continuous mapping, and let \(B:E\to R^ n\) be a bounded linear mapping onto a euclidean space. The solutions (y,\(\lambda)\) to the problem: \(Ly=H(y,\lambda)\), \(By=0\) can be represented as the fixed points of a mapping \(T:E\times R^ n\to E\times R^ n\). Nielsen fixed point theory may be extended to produce lower bounds for the number of fixed points of such maps. A typical problem to which the theory applies is a ''three-point boundary value problem'' \(y=y(t):[0,1]\to R^ n\) and \(\lambda \in R^ n\) which solves \(y''=h(t,y,y',\lambda)\) such that \(y(0)=y(1/2)=y(1)=0\).
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 3996478
zbMATH Keywords: Nielsen number
zbMATH Keywords: retraction
zbMATH Keywords: retractible map
zbMATH Keywords: Leray-Schauder boundary condition
zbMATH Keywords: parametrized differential equation
zbMATH Keywords: Nielsen fixed point theory
zbMATH Keywords: three-point boundary value problem
zbMATH Keywords: second-order ordinary differential system
MaRDI profile type: Publication
full work available at URL: pjm.1988.131.51
OpenAlex ID: W2026858527
DOI: 10.2140/PJM.1988.131.51
description: scientific article; zbMATH DE number 3996478