Ayrık Olmayan Sınır Koşullarına Sahip Ters Nodal Problem İçin Teklik Teoremi

Year 2025, Volume: 15 Issue: 3, 27 - 32, 19.11.2025

Merve Arslantaş

Abstract

Bu araştırma, sonlu bir aralıkta, aralık içinde süreksizliğe sahip ikinci dereceden diferansiyel operatörler için ters nodal problemi araştırmaktadır. Daha önce yapılan benzer çalışmalarda süreksizlik noktası parçanın orta noktası iken benzer sonuçlar elde edilmiştir. Parçanın orta noktası süreksizlik noktası olarak alındığında özdeğer ve özfonksiyonların asimptotik ifadelerinin, literatürde bilinen klasik ayrık sınır koşulları ile verilen problemlerin özdeğer ve özfonksiyonlarının asimptotiklerinden pek de farklı olmadığı görülmektedir. Sunulan çalışmada ise verilen ters nodal problemin çözümü için süreksizlik noktalarının tipi belirlenmiştir. R={a_r: a_r=rπ r∈(0,1)∩Q} kümesine ait her a_r süreksizlik noktası için çalışma, ters nodal problemin çözümünün varlığını kanıtlar ve çözümün belirlenmesi için pratik bir yöntem sunar.

Keywords

Süreksizlik koşulları , nodal noktalar , Sturm-Liouville denklemi

Uniqueness Theorem For Inverse Nodal Problem With Nonseparable Boundary Conditions

Abstract

This research investigates the inverse nodal reconstruction for second-order differential operators on a bounded interval, incorporating discontinuities within that interval. In previous similar studies, when the discontinuity point was at the midpoint of the part, similar results were obtained. When the midpoint of the part is taken as the discontinuity point, it is observed that the asymptotic expressions of the eigenvalues and eigenfunctions do not differ significantly from those of problems with classical separated boundary conditions known in the literature. In the presented study, the type of discontinuity points has been determined for the solution of the given inverse nodal problem. For every discontinuity point a_r belonging to the set R={a_r: a_r=rπ r∈(0,1)∩Q} the study establishes the existence of a solution to the inverse nodal problem and offers a practical method for its determination.

Keywords

Discontinuous conditions , nodal points , Sturm-Louville equation

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