A Prüfer angle approach to semidefinite Sturm–Liouville problems with coupling boundary conditions

It is shown how to reduce the periodic/antiperiodic Sturm–Liouville problems to analysis of the Prüfer angle. This provides an alternative to the more usual approaches via operator theory or the Hill discriminant in the definite case, and leads to new results in the semidefinite case. An extension to more general coupling boundary conditions is also given.