S. Cuccagna and D. Pelinovsky

Bifurcations from the endpoints of the essential spectrum in the linearized nonlinear Schrodinger problem

Journal of Mathematical Physics, 46, 053520 (2005)

Abstract:
We study bifurcations of eigenvalues from the endpoints of the essential spectrum in the linearized nonlinear Schrodinger problem in three dimensions. We show that a resonance and an eigenvalue of positive energy at the endpoint may bifurcate only to a realeigenvalue of positive energy, while an eigenvalue of negative energy at the endpoint may also bifurcate to complex eigenvalues.

Keywords:
SPECTRAL THEORY, NONLINEAR SCHRODINGER EQUATION, EMBEDDED EIGENVALUES, END POINTS, RESONANCES, BIFURCATIONS OF EIGENVALUES AND RESONANCES