On the perturbed eigenvalue problem
type: Item
instance of: scholarly article
title: On the perturbed eigenvalue problem
zbMATH Open document ID: 0819.47027
author: Eckart W. Gekeler
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-08-17T00:00:00Z
review text: The author considers the perturbed eigenvalue problem \(L(x) v(x)= \lambda(x) v(x)\) near \(0= x\in \mathbb{R}\) with \(L(x)\) a Fredholm operator of index zero. Using the implicit function theorem and the bordering lemma, he derives a necessary and sufficient smoothness condition for the characteristic pairs \((\lambda(x), v(x))\) with eigenvalue \(\lambda(x)\) emanating from a semi-simple eigenvalue \(\lambda(0)\) of \(L(0)\).
Mathematics Subject Classification ID: 47A75
Mathematics Subject Classification ID: 47A55
zbMATH DE Number: 755529
zbMATH Keywords: perturbed eigenvalue problem
zbMATH Keywords: Fredholm operator of index zero
zbMATH Keywords: implicit function theorem
zbMATH Keywords: bordering lemma
MaRDI profile type: Publication
OpenAlex ID: W1993437672
DOI: 10.1006/JMAA.1995.1147
description: scientific article; zbMATH DE number 755529