On Threshold Eigenvalues and Resonances for the Linearized NLS Equation
University of Toronto, Department of Mathematics,
Toronto, ON, M5S
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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
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