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

Elif Başkaya; Süleyman Şengül; Elif Başkaya; Süleyman Şengül

doi:10.3934/math.2025971

AIMS Mathematics

2025, Volume 10, Issue 9: 21835-21852. doi: 10.3934/math.2025971

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Research article

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

Elif Başkaya ¹,
Süleyman Şengül ^{2
,
,}

1.
Department of Mathematics, Faculty of Science, Karadeniz Technical University, Trabzon 61080, Türkiye
2.
Department of Mathematics, Faculty of Arts and Sciences, Recep Tayyip Erdoğan University, Rize 53100, Türkiye

Received: 07 July 2025 Revised: 08 September 2025 Accepted: 11 September 2025 Published: 19 September 2025
MSC : 34B09, 34B30, 34L15

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.
- integrable potential,
- spectral parameter,
- boundary value problems,
- asymptotic estimates
Citation: Elif Başkaya, Süleyman Şengül. On symmetric potential in a boundary value problem dependent on an eigenparameter[J]. AIMS Mathematics, 2025, 10(9): 21835-21852. doi: 10.3934/math.2025971

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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.

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