An estimate on the number of bound states of Schrödinger operators
type: Item
instance of: scholarly article
title: An estimate on the number of bound states of Schrödinger operators
zbMATH Open document ID: 0853.35081
author: Kunihiko Sugimura
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-07-14T00:00:00Z
review text: The author investigates the eigenvalue problem \[ (- \Delta+ V(x)) u= \lambda u\quad \text{on } \Omega,\quad u|_{\partial\Omega}= 0,\tag{1} \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^2\) and \(V\) is a measurable function defined on \(\Omega\). The main result of the paper is that the number of non-positive eigenvalues of problem (1) \(N(V, \Omega)\) is bounded by \(N(V, \Omega)\leq C \int_\Omega V_-(1+ \log^+ V_-) dx\), where \(C\) is a positive constant depending only on \(\Omega\) and \(V_-\) is the negative part of \(V\). The author uses some ideas of the technique of K. Tanaka as well as the extrapolation theorem of O. N. Capri and N. A. Fava.
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 902528
zbMATH Keywords: number of non-positive eigenvalues
reviewed by: Emil Minchev
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0129
OpenAlex ID: W2010974323
DOI: 10.1006/JMAA.1996.0129
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description: scientific article; zbMATH DE number 902528