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