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

Başkaya E., Şengül S.

AIMS MATHEMATICS, vol.10, no.9, pp.21835-21852, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 9
  • Publication Date: 2025
  • Doi Number: 10.3934/math.2025971
  • Journal Name: AIMS MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Page Numbers: pp.21835-21852
  • Keywords: asymptotic estimates, boundary value problems, integrable potential, spectral parameter
  • Karadeniz Technical University Affiliated: Yes

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.