Bifurcation for the solutions of equations involving set valued mappings
type: Item
instance of: scholarly article
title: Bifurcation for the solutions of equations involving set valued mappings
zbMATH Open document ID: 0582.47048
DOI: 10.1155/S0161171285000035
author: Bevan Thompson
author: E. Tarafdar
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46007
review text: We prove bifurcation results for set valued equations of the form \(x\in \mu Ax+R(x,\mu)\), where \(A: X\to X\) is compact linear and R is a compact, convex valued compact mapping which is \(o(\| x\|)\) uniformly in \(\mu\) in compact intervals and some bounded open neighbourhood of zero in X. Our results extend the theorem of Krasnosel'skii and Rabinowitz concerning bifurcation from \((0,\mu_ 0)\), where \(\mu_ 0\) is a characteristic value of A of odd multiplicity. The results are applied to a two point boundary value problem.
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47A50
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 3931850
zbMATH Keywords: bifurcation results for set valued equations
zbMATH Keywords: compact, convex valued compact mapping
zbMATH Keywords: two point boundary value problem
MaRDI profile type: Publication
OpenAlex ID: W1995286800
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description: scientific article; zbMATH DE number 3931850