Relative Oscillation–Non-Oscillation Criteria for Perturbed Periodic Dirac Systems

Under minimal hypotheses, sufficient criteria for a perturbed Dirac system to be relatively oscillatory or non-oscillatory at ∞ with respect to a reference equation with periodic coefficients are proved my means of an asymptotic analysis of generalized Prüfer angles. As illustrated by an example, they help decide whether the number of eigenvalues in gaps of the essential spectrum is finite or infinite. The critical perturbations naturally occur in the partial-wave analysis of spherically symmetric Dirac operators