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Bifurcations from the endpoints of the essential spectrum in the linearized nonlinear Schrödinger problem. (English) Zbl 1110.35082

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

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
47J15 Abstract bifurcation theory involving nonlinear operators
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