Guaranteed error bounds for eigenvalues of singular Sturm-Liouville problems

We develop a simple oscillation theory for singular Sturm-Liouville problem s and combine it with recent asymptotic results, and with the AWA interval- arithmetic code for integration of initial value problems with guaranteed e rror bounds, to obtain eigenvalue approximations with guaranteed error boun ds for a class of singular Sturm-Liouville problems. We believe that this i s the first time that this has been achieved for singular eigenvalue proble ms.