Relative oscillation -- non-oscillation criteria for perturbed periodic Dirac systems
The author considers radial Dirac operators and gives criteria on perturbations of the coefficients which ensure that the solutions to the perturbed problem are ``relatively nonoscillatory'' in the sense that the difference between the Prüfer angles of the solutions to the perturbed and unperturbed problems remains bounded. As an application, results of \textit{M. Klaus} [On the point spectrum of Dirac operators, Helv. Phys. Acta 53, No. 3, 453-462 (1980)] on the finiteness of the number of eigenvalues for the potential \(-c/(1+r^2)\), \(0<c<1/8\), are extended to the borderline case \(c=1/8\) [see also \textit{M. Griesemer} and \textit{J. Lutgen}, J. Funct. Anal. 162, No. 1, 120-134 (1999; Zbl 0926.34074)]. The argument leans on previous work by the author, especially [Commun. Math. Phys. 211, No. 2, 465-485 (2000; Zbl 0953.34069)].
scientific article; zbMATH DE number 1496312
scientific article