Nonlinear eigenvalues problems with a small parameter
type: Item
instance of: scholarly article
title: Nonlinear eigenvalues problems with a small parameter
zbMATH Open document ID: 0548.35094
DOI: 10.1007/BF01200376
published in: Integral Equations and Operator Theory
publication date: 1984-01-01T00:00:00Z
review text: In this work we study nonlinear eigenvalues problems like \([-\sigma^ 2d^ 2/dt^ 2+(t^ 2-\mu)^ 2+1]u=0\) where \(\mu \in {\mathbb{C}}\), \(\sigma >0\), \(u\in {\mathcal S}({\mathbb{R}}^ n)\). More precisely we study the spectrum of the operator \(Q(\sigma;\mu)=-\sigma^ 2d^ 2/dt^ 2+(t^ 2-\mu)^ 2+1\) when \(\sigma \to 0\), \(\sigma >0\). Our method of proof consists in replacing our problem by a linear eigenvalue problem about a non self adjoint system.
Mathematics Subject Classification ID: 35P30
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 3873881
zbMATH Keywords: small parameter
zbMATH Keywords: nonlinear eigenvalues problems
zbMATH Keywords: spectrum
author: Didier Robert
MaRDI profile type: Publication
cites work: Régularité analytique pour des opérateurs elliptiques singuliers en un point
cites work: Q5336643
cites work: Comportement semi-classique du spectre des hamiltoniens quantiques elliptiques
cites work: Q5631640
cites work: On some mathematical principles in the linear theory of damped oscillations of continua I
cites work: Sur un problème aux valeurs propres non linéaire
cites work: Proprietes spectrales d'operators pseduo-differentiels
full work available at URL: https://doi.org/10.1007/bf01200376
OpenAlex ID: W2018389952
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description: scientific article; zbMATH DE number 3873881