Perturbation Results of Limit point case and Limit circle case of Sturm-Liouville Differential Operators

摘要

Sufficient conditions for invariance of limit point case (limit circle case) for the Sturm-Liouville differential operator τ = − d2 dx2 + q at a singular point under perturbation have been determined. In particular it is proved that under bounded below perturbation limit point case (limit circle case) for the Sturm-Liouville differential operator at a singular point remains invariant.