Three-term spectral asymptotics for nonlinear Sturm-Liouville problems
type: Item
instance of: scholarly article
title: Three-term spectral asymptotics for nonlinear Sturm-Liouville problems
zbMATH Open document ID: 1019.34029
author: Tetsutaro Shibata
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2002-12-01T00:00:00Z
review text: Here, the nonlinear Sturm-Liouville problem \[ -u''(t)+|u(t)|^{p-1}u(t)+f(u(t))=\lambda u(t),\quad u(0)=0,\quad u(1)=0, \] is considered on the interval \((0,1)\). The main result deals with a three-term asymptotic formula for the \(n\)th eigencurve \(\lambda_n(\alpha)\) (associated with the eigenfunction \(u_{n,\alpha}\) with \(n-1\) simple interior zeros and \(\|u_{n,\alpha}\|_2=\alpha)\) as \(\alpha\to +\infty\) and for the width of the boundary layer of \(u_{n,\alpha}\) as \(\alpha\to +\infty\). Furthermore, there is also proved that if the function \(f\) is of a special type, the assumptions that the main result holds can be weakened.
reviewed by: Robert Hakl
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1836997
zbMATH Keywords: three-term spectral asymptotics
zbMATH Keywords: nonlinear Sturm-Liouville
zbMATH Keywords: width of boundary layer
MaRDI profile type: Publication
full work available at URL: s00030-002-8126-9
OpenAlex ID: W2090731622
DOI: 10.1007/S00030-002-8126-9
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description: scientific article; zbMATH DE number 1836997