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On Threshold Eigenvalues and Resonances for the Linearized NLSEquation

Published online by Cambridge University Press:  12 May 2010

V. Vougalter
V. Vougalter*
Affiliation:
University of Toronto, Department of Mathematics, Toronto, ON, M5S 2E4, Canada
*
* E-mail: vitali@math.toronto.edu
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Abstract

We prove the instability of threshold resonances and eigenvalues of the linearized NLSoperator. We compute the asymptotic approximations of the eigenvalues appearing from theendpoint singularities in terms of the perturbations applied to the original NLS equation.Our method involves such techniques as the Birman-Schwinger principle and the Feshbachmap.

Keywords

NLS equationspectral stabilityBirman-Schwinger principleFeshbach map
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 4: Spectral problems. Issue dedicated to the memory of M. Birman , 2010 , pp. 448 - 469
Copyright
© EDP Sciences, 2010

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