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

S. M. Padhye; K. J. Shinde

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

S. M. Padhye¹ , K. J. Shinde^2*

Head, Dept. Of Mathematics, Shri RLT College of Science, Akola 444 104 (M.S.), India
Research Scholar, Sant Gadge Baba Amravati University, Amravati (M.S.), India

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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.

Keywords

limit point case, limit circle case, singular point

INTRODUCTION

We study the Sturm – Liouville differential operator is of the form

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