Existence and Uniqueness of Solutions in Inverse Sturm-Liouville Problems

Year 2023, Volume: 2023 Issue: 19, 19 - 26, 03.01.2024

Münevver Tuz

Abstract

In this article, we examined a boundary value problem for the Sturm-Liouville equation defined in the interval [0, L]. The problem with [0, L] corresponds to the small vibrations of a fixed-end straight rope. In these problems, the necessary and sufficient conditions for the unique determination of the potential by only one spectrum at certain parameters of the boundary conditions are investigated. For the inverse problem, it has been examined that the spectrum is effective in describing the potential of the Sturm-Liouville problem alone, thus the intensity of the array. Also, the uniqueness results of this problem are proved using the Leray-Schauder fixed point theorem in a Banach space. Thus, with a different method, an existence and uniqueness result was created for the problem with these boundary conditions.

Keywords

Sturm-Liouville problem, boundary conditions, Leray–Schauder, eigenvalue, spectrum.

Supporting Institution

ICEANS 2022 konferans (Kasım)

Project Number

no

Thanks

I would like to express my gratitude to all the referees and editors for their valuable comments and suggestions that improve the quality of this article.

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