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On threshold eigenvalues and resonances for the linearized NLS equation. (English) Zbl 1193.35212
Summary: 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.

MSC:
35Q55NLS-like (nonlinear Schrödinger) equations
47J15Abstract bifurcation theory
81Q05Closed and approximate solutions to quantum-mechanical equations
81Q10Selfadjoint operator theory in quantum theory, including spectral analysis
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