2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174452We present a streamlined approach to relative oscillation criteria based on effective Pruefer 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 the Gesztesy-Uenal 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.22 pagesSpectral TheoryMathematical Physics34C10, 34B24 (Primary); 34L20, 34L05 (Secondary)text