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Research Article | Open Access

On symmetric potential in a boundary value problem dependent on an eigenparameter

Elif Başkaya1, Süleyman Şengül2( )
Department of Mathematics, Faculty of Science, Karadeniz Technical University, Trabzon 61080, Türkiye
Department of Mathematics, Faculty of Arts and Sciences, Recep Tayyip Erdoğan University, Rize 53100, Türkiye
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Abstract

In this work, we asymptotically calculate the eigenvalue of a boundary value problem that involves an integrable and symmetric potential over a defined interval and includes eigenvalues in the boundary conditions. We apply the Riccati equation to derive the asymptotic solutions. To validate our findings, we compare them with numerical results obtained using the element–free Galerkin method. The comparison confirms the consistency and accuracy of the asymptotic approach.

Keywords

integrable potentialspectral parameterboundary value problemsasymptotic estimates
CLC number: 34B09, 34B30, 34L15

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AIMS Mathematics
Volume 10 Issue 9,
September 2025
Pages 21835-21852
DOI: 10.3934/math.2025971

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Cite this article:
Başkaya E, Şengül S. On symmetric potential in a boundary value problem dependent on an eigenparameter. AIMS Mathematics, 2025, 10(9): 21835-21852. https://doi.org/10.3934/math.2025971

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Received: 07 July 2025
Revised: 08 September 2025
Accepted: 11 September 2025
Published: 19 September 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)