J. Differential Equations 245, 3823-3848 (2008) [DOI: 10.1016/j.jde.2008.06.004]

Effective Prüfer Angles and Relative Oscillation Criteria

Helge Krüger and Gerald Teschl

We present a streamlined approach to relative oscillation criteria based on effective Prüfer angles adapted to the use at the edges of the essential spectrum.

Based on this we provided a new scale of oscillation criteria for general Sturm-Liouville operators which answer the question whether a perturbation inserts a finite or an infinite number of eigenvalues into an essential spectral gap. As a special case we recover and generalize the Gesztesy-Ünal criterion (which works below the spectrum and contains classical criteria by Kneser, Hartman, Hille, and Weber) and the well-known results by Rofe-Beketov including the extensions by Schmidt.

MSC2000: Primary 34C10, 34B24; Secondary 34L20, 34L05
Keywords: Sturm-Liouville operators, oscillation theory

TeX file (65k) or pdf file (337k)