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birman-schwinger principle

Mathematical Modelling of Natural Phenomena (1)

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On Threshold Eigenvalues and Resonances for the Linearized NLSEquation
V. Vougalter
Journal:

Mathematical Modelling of Natural Phenomena / Volume 5 / Issue 4 / 2010

Published online by Cambridge University Press:

12 May 2010, pp. 448-469

Print publication:

2010
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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.