Uniqueness Theorem For Inverse Nodal Problem With Nonseparable Boundary Conditions

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Karaelmas Fen ve Mühendislik Dergisi
Cilt: 15 Sayı: 3
Uniqueness Theorem For Inverse Nodal Problem With Nonseparable Boundary Conditions

Uniqueness Theorem For Inverse Nodal Problem With Nonseparable Boundary Conditions

Authors : Merve Arslantaş

Pages : 27-32

Doi:10.7212/karaelmasfen.1657961

View : 99 | Download : 170

Publication Date : 2025-11-19

Article Type : Research Paper

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 : Süreksizlik koşulları, nodal noktalar, Sturm-Liouville denklemi

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