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An Estimate on the Number of Bound States of Schrödinger Operators

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
199
Issue
1
Identifiers
DOI: 10.1006/jmaa.1996.0129

Abstract

Abstract This paper is concerned with the eigenvalue problem (−Δ+ V( x)) u=λ uon Ω and u| ∂Ω=0, where Ω is a bounded domain in R 2and Vis a suitable function defined on Ω. We prove that the number of non-positive eigenvalues of the preceding problem is bounded by const. ∫ Ω V −(1+log + V −) dx, where V −is the negative part of V.

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