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

Abstract

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.

S. M. Padhye , K. J. Shinde

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