| Issue |
Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010
Spectral problems. Issue dedicated to the memory of M. Birman
|
|
|---|---|---|
| Page(s) | 448 - 469 | |
| DOI | https://doi.org/10.1051/mmnp/20105417 | |
| Published online | 12 May 2010 | |
On Threshold Eigenvalues and Resonances for the Linearized NLS Equation
University of Toronto, Department of Mathematics,
Toronto, ON, M5S
2E4, Canada
* E-mail: vitali@math.toronto.edu
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.
Mathematics Subject Classification: 35Q55 / 47J15 / 81Q05
Key words: NLS equation / spectral stability / Birman-Schwinger principle / Feshbach map
© EDP Sciences, 2010
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