Classification of Sturm-Liouville Operators With Beta-Derivatives at the Limit-Point

Abstract

The singular Beta-Sturm-Liouville operator Ω(y) = −Tβ( f (t) Tβ y(t)) + g(t)y(t) on [0,∞) is taken into consideration in this study. A criterion for Weyl's limit-point classification is given for this operator. For this purpose, firstly the basic concepts of beta calculation and some theorems are given. Using Everit's method (1966), it is shown under what conditions the Beta-Sturm-Liouville equation will be in its limit-point case.

Keywords

• Limit-point case
• singular Sturm-Liouville operator
• beta-Sturm-Liouville problem
• limit-point classification

Sınır noktasında Beta Türevli Sturm-Liouville Operatörlerinin Sınıflandırılması

Öz

Bu çalışmada tekil Beta-Sturm-Liouville operatörü Ω(y) = −Tβ( f (t) Tβ y(t)) + g(t)y(t) on [0,∞) ele alınmıştır. Bu operatör için Weyl'in sınır noktası sınıflandırmasına yönelik bir kriter verilmiştir. Bu amaçla öncelikle beta hesabının temel kavramları ve bazı teoremler verilmiştir. Everit yöntemi (1966) kullanılarak Beta-Sturm-Liouville denkleminin sınır noktası durumunda hangi koşullar altında olacağı gösterilmiştir.

Anahtar Kelimeler

• Sınır nokyası durumu
• Tekil Sturm-Liouville operatörü
• beta-Sturm-Liouville problemi
• sınır noktası sınırlandırması

Kaynakça

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