On Threshold Eigenvalues and Resonances for the Linearized NLS Equation

V. Vougalter¹

¹ University of Toronto, Department of Mathematics, Toronto, ON, M5S 2E4, Canada

Mathematical modelling of natural phenomena, Tome 5 (2010) no. 4, pp. 448-469.

Résumé

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

Détail

DOI : 10.1051/mmnp/20105417

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