Note on a nonlinear eigenvalue problem
type: Item
instance of: scholarly article
title: Note on a nonlinear eigenvalue problem
zbMATH Open document ID: 0785.34050
author: Peter Lindqvist
published in: Rocky Mountain Journal of Mathematics
publication date: 1993-08-17T00:00:00Z
review text: Consider the nonlinear eigenvalue problem \({d \over dx} (| u' |^{p-2}u')+ \lambda | u |^{p-2}u=0\). It is observed that the first positive eigenvalue \(\lambda_ p\) satisfies a conjugacy condition \(\lambda_ p^{1/p}=\lambda_ q^{1/p}\), \({1 \over p} + {1 \over q}=1\). Also the corresponding eigenfunctions are related. Similar results hold for the higher eigenvalues and eigenvectors.
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B99
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 218645
zbMATH Keywords: nonlinear eigenvalue problem
zbMATH Keywords: conjugacy condition
zbMATH Keywords: eigenfunctions
reviewed by: Ludwig Elsner
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072623
OpenAlex ID: W2093969139
cites work: Bifurcation Phenomena Associated to the p-Laplace Operator
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DOI: 10.1216/RMJM/1181072623
description: scientific article; zbMATH DE number 218645