Sınır Koşulunda Öz Parametre Bulunduran Bir Sturm-Liouville Operatörü İçin Ters Nodal Problem

Year 2020, , 601 - 609, 15.07.2020

Sertaç Göktaş

https://doi.org/10.17714/gumusfenbil.672966

Abstract

Bu çalışmada, sınır koşulunda öz parametre ve ikinci
derece diferensiyel denkleminde birden fazla potansiyel bulunduran bir Sturm-
Liouville problemi ele alınmıştır. Prüfer dönüşümü yardımıyla bu problemin özdeğerlerinin
ve nodal parametrelerinin asimptotik formülleri bulunmuştur. Ayrıca, potansiyel
fonksiyonlar için bir yapılandırma formülü elde edilmiştir.

Keywords

Nodal Noktalar, Nodal Uzunluklar, Potansiyel Fonksiyon, Prüfer Dönüşümü

Inverse Nodal Problem for A Sturm-Liouville Operator with Eigenparameter in the Boundary Condition

Abstract

In this
study, Sturm-Liouville problem with eigenparameter in the boundary condition
and more than one potential in the second order differential equation is
considered. Asymptotic formulas of the eigenvalues and nodal parameters of this
problem are found by Prüfer substitution. In addition, a reconstruction formula
is obtained for potential functions.

Keywords

Nodal Points, Nodal Lengths, Potential Function

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