Research Article

On the Eigenvalue Problems with Integrable Potential and Boundary Conditions Rationally Dependent on the Eigenparameter

Volume: 2 Number: 2 July 31, 2025

On the Eigenvalue Problems with Integrable Potential and Boundary Conditions Rationally Dependent on the Eigenparameter

Abstract

We present the asymptotic estimates of the eigenvalues for an eigenvalue problem that the problem has also the eigenparameter in the second boundary condition, rationally. The potential of the problem is integrable.

Keywords

References

  1. Binding P. A., Browne P. J. and Watson B. A., 2004. Equivalence of Inverse Sturm-Liouville Problems with Boundary Conditions Rationally Dependent on the Eigenparameter. Journal of Mathematical Analysis and Applications, 291, 246-261.
  2. Coşkun H. and Başkaya E., 2010. Asymptotics of eigenvalues for regular Sturm-Liouville problems with eigenvalue parameter in the boundary condition for integrable potential. Mathematica Scandinavica, 107, 209-223.
  3. Coşkun H., Başkaya E. and Kabataş A., 2019. Instability intervals for Hill’s equation with symmetric single well potential. Ukrainian Mathematical Journal, 71 (6), 977-983.
  4. Coşkun H. and Kabataş A., 2013. Asymptotic approximations of eigenfunctions for regular Sturm-Liouville problems with eigenvalue parameter in the boundary condition for integrable potential. Mathematica Scandinavica, 113 (1), 143-160.
  5. Coşkun H. and Kabataş A., 2016. Green’s function of regular Sturm-Liouville problem having eigenparameter in one boundary condition. Turkish Journal of Mathematics and Computer Science, 4, 1–9.
  6. Coşkun H., Kabataş A. and Başkaya E., 2017. On Green’s function for boundary value problem with eigenvalue dependent quadratic boundary condition. Boundary Value Problems, 71.
  7. Harris B. J., 1997. The Form of the Spectral Functions Associated with Sturm-Liouville Problems with Continuous Spectrum. Mathematika, 44 (1), 149-161.
  8. Kabataş A., 2022. On eigenfunctions of Hill’ s equation with symmetric double well potential. Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics, 71 (3), 634-649.

Details

Primary Language

English

Subjects

Approximation Theory and Asymptotic Methods

Journal Section

Research Article

Authors

Publication Date

July 31, 2025

Submission Date

May 31, 2025

Acceptance Date

June 17, 2025

Published in Issue

Year 2025 Volume: 2 Number: 2

APA
Başkaya, E. (2025). On the Eigenvalue Problems with Integrable Potential and Boundary Conditions Rationally Dependent on the Eigenparameter. Hitit Journal Of Science, 2(2), 37-41. https://izlik.org/JA78NT58SF
AMA
1.Başkaya E. On the Eigenvalue Problems with Integrable Potential and Boundary Conditions Rationally Dependent on the Eigenparameter. HJS. 2025;2(2):37-41. https://izlik.org/JA78NT58SF
Chicago
Başkaya, Elif. 2025. “On the Eigenvalue Problems With Integrable Potential and Boundary Conditions Rationally Dependent on the Eigenparameter”. Hitit Journal Of Science 2 (2): 37-41. https://izlik.org/JA78NT58SF.
EndNote
Başkaya E (July 1, 2025) On the Eigenvalue Problems with Integrable Potential and Boundary Conditions Rationally Dependent on the Eigenparameter. Hitit Journal Of Science 2 2 37–41.
IEEE
[1]E. Başkaya, “On the Eigenvalue Problems with Integrable Potential and Boundary Conditions Rationally Dependent on the Eigenparameter”, HJS, vol. 2, no. 2, pp. 37–41, July 2025, [Online]. Available: https://izlik.org/JA78NT58SF
ISNAD
Başkaya, Elif. “On the Eigenvalue Problems With Integrable Potential and Boundary Conditions Rationally Dependent on the Eigenparameter”. Hitit Journal Of Science 2/2 (July 1, 2025): 37-41. https://izlik.org/JA78NT58SF.
JAMA
1.Başkaya E. On the Eigenvalue Problems with Integrable Potential and Boundary Conditions Rationally Dependent on the Eigenparameter. HJS. 2025;2:37–41.
MLA
Başkaya, Elif. “On the Eigenvalue Problems With Integrable Potential and Boundary Conditions Rationally Dependent on the Eigenparameter”. Hitit Journal Of Science, vol. 2, no. 2, July 2025, pp. 37-41, https://izlik.org/JA78NT58SF.
Vancouver
1.Elif Başkaya. On the Eigenvalue Problems with Integrable Potential and Boundary Conditions Rationally Dependent on the Eigenparameter. HJS [Internet]. 2025 Jul. 1;2(2):37-41. Available from: https://izlik.org/JA78NT58SF