Research Article
BibTex RIS Cite

ON SOME ASYMPTOTIC EIGENVALUES OF HILL' S EQUATION

Year 2024, , 23 - 30, 29.12.2024
https://doi.org/10.33773/jum.1557752

Abstract

In this paper, we deal with Hill' s equation with symmetric single well potential. We find the lower and upper boundaries of the difference between Dirichlet and Neumann eigenvalues of Hill' s equation. We also calculate the eigenvalues of Hill' s equation with two mixed problems, asymptotically.

References

  • E. Baskaya, Periodic and semi-periodic eigenvalues of Hill' s equation with symmetric double well potential, Turkic World Mathematical Society Journal of Applied and Engineering Mathematics, vol.10, N.2, pp.346-352 (2020).
  • E. Baskaya, Asymptotics of Eigenvalues for Regular Sturm-Liouville Problems with Spectral Parameter-Dependent Boundary Conditions and Symmetric Single Well Potential, Turkish Journal of Mathematics and Computer Science, vol.13, N.1, pp.44-50 (2021).
  • E. Baskaya, On the asymptotics of eigenvalues for a Sturm-Liouville problem with symmetric single well potential, Demonstratio Mathematica, vol.57, N. 1, pp. 20230129 (2024).
  • A. Cabada, J. A. Cid and L. Lopez-Somoza, Green's functions and spectral theory for the Hill' equation, Applied Mathematics and Computation, vol.286, pp. 88-105 (2016).
  • H. Coskun and E. Baskaya, Asymptotics of eigenvalues of regular Sturm-Liouville problems with eigenvalue parameter in the boundary condition for integrable potential, Mathematica Scandinavica, vol.107, N.2, pp.209–223 (2010).
  • H. Coskun and N. Bayram, Asymptotics of eigenvalues for regular Sturm–Liouville problems with eigenvalue parameter in the boundary condition, Journal of Mathematical Analysis and Applications, vol.306, N.2, pp.548-566 (2005).
  • H. Coskun and A. Kabatas, Asymptotic approximations of eigenfunctions for regular Sturm-Liouville problems with eigenvalue parameter in the boundary condition for integrable potential, Mathematica Scandinavica, vol.113, N.1, pp.143-160 (2013).
  • H. Coskun and A. Kabatas, Green’s Function of Regular Sturm-Liouville Problem Having Eigenparameter in One Boundary Condition, Turkish Journal of Mathematics and Computer Science, vol.4, pp.1–9 (2016).
  • H. Coskun, A. Kabatas and E. Baskaya, On Green’s function for boundary value problem with eigenvalue dependent quadratic boundary condition, Boundary Value Problems, vol.71, (2017).
  • H. Coskun, E. Baskaya and A. Kabatas, Instability intervals for Hill’s equation with symmetric single well potential, Ukrainian Mathematical Journal, vol.71, N. 6, pp.977-983 (2019).
  • M. S. P. Eastham, The spectral theory of periodic differential equations, Scottish Academic Press, Edinburgh and London, (1973).
  • A. Kabatas, On eigenfunctions of Hill' s equation with symmetric double well potential, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol.71, N.3, pp.634-649 (2022).
  • A. Kabatas, Eigenfunction and Green' s Function Asymptotics for Hills Equation with Symmetric Single-Well Potential, Ukrainian Mathematical Journal, vol.74, N.2, pp.218-231 (2022).
  • A. Kabatas, One boundary value problem including a spectral parameter in all boundary conditions, Opuscula Mathematica, vol.43, N.5, pp.651-661 (2023).
Year 2024, , 23 - 30, 29.12.2024
https://doi.org/10.33773/jum.1557752

Abstract

References

  • E. Baskaya, Periodic and semi-periodic eigenvalues of Hill' s equation with symmetric double well potential, Turkic World Mathematical Society Journal of Applied and Engineering Mathematics, vol.10, N.2, pp.346-352 (2020).
  • E. Baskaya, Asymptotics of Eigenvalues for Regular Sturm-Liouville Problems with Spectral Parameter-Dependent Boundary Conditions and Symmetric Single Well Potential, Turkish Journal of Mathematics and Computer Science, vol.13, N.1, pp.44-50 (2021).
  • E. Baskaya, On the asymptotics of eigenvalues for a Sturm-Liouville problem with symmetric single well potential, Demonstratio Mathematica, vol.57, N. 1, pp. 20230129 (2024).
  • A. Cabada, J. A. Cid and L. Lopez-Somoza, Green's functions and spectral theory for the Hill' equation, Applied Mathematics and Computation, vol.286, pp. 88-105 (2016).
  • H. Coskun and E. Baskaya, Asymptotics of eigenvalues of regular Sturm-Liouville problems with eigenvalue parameter in the boundary condition for integrable potential, Mathematica Scandinavica, vol.107, N.2, pp.209–223 (2010).
  • H. Coskun and N. Bayram, Asymptotics of eigenvalues for regular Sturm–Liouville problems with eigenvalue parameter in the boundary condition, Journal of Mathematical Analysis and Applications, vol.306, N.2, pp.548-566 (2005).
  • H. Coskun and A. Kabatas, Asymptotic approximations of eigenfunctions for regular Sturm-Liouville problems with eigenvalue parameter in the boundary condition for integrable potential, Mathematica Scandinavica, vol.113, N.1, pp.143-160 (2013).
  • H. Coskun and A. Kabatas, Green’s Function of Regular Sturm-Liouville Problem Having Eigenparameter in One Boundary Condition, Turkish Journal of Mathematics and Computer Science, vol.4, pp.1–9 (2016).
  • H. Coskun, A. Kabatas and E. Baskaya, On Green’s function for boundary value problem with eigenvalue dependent quadratic boundary condition, Boundary Value Problems, vol.71, (2017).
  • H. Coskun, E. Baskaya and A. Kabatas, Instability intervals for Hill’s equation with symmetric single well potential, Ukrainian Mathematical Journal, vol.71, N. 6, pp.977-983 (2019).
  • M. S. P. Eastham, The spectral theory of periodic differential equations, Scottish Academic Press, Edinburgh and London, (1973).
  • A. Kabatas, On eigenfunctions of Hill' s equation with symmetric double well potential, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol.71, N.3, pp.634-649 (2022).
  • A. Kabatas, Eigenfunction and Green' s Function Asymptotics for Hills Equation with Symmetric Single-Well Potential, Ukrainian Mathematical Journal, vol.74, N.2, pp.218-231 (2022).
  • A. Kabatas, One boundary value problem including a spectral parameter in all boundary conditions, Opuscula Mathematica, vol.43, N.5, pp.651-661 (2023).
There are 14 citations in total.

Details

Primary Language English
Subjects Ordinary Differential Equations, Difference Equations and Dynamical Systems
Journal Section Research Article
Authors

Elif Başkaya 0000-0001-6118-9183

Publication Date December 29, 2024
Submission Date September 29, 2024
Acceptance Date November 2, 2024
Published in Issue Year 2024

Cite

APA Başkaya, E. (2024). ON SOME ASYMPTOTIC EIGENVALUES OF HILL’ S EQUATION. Journal of Universal Mathematics, 7(To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI"), 23-30. https://doi.org/10.33773/jum.1557752
AMA Başkaya E. ON SOME ASYMPTOTIC EIGENVALUES OF HILL’ S EQUATION. JUM. December 2024;7(To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI"):23-30. doi:10.33773/jum.1557752
Chicago Başkaya, Elif. “ON SOME ASYMPTOTIC EIGENVALUES OF HILL’ S EQUATION”. Journal of Universal Mathematics 7, no. To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI" (December 2024): 23-30. https://doi.org/10.33773/jum.1557752.
EndNote Başkaya E (December 1, 2024) ON SOME ASYMPTOTIC EIGENVALUES OF HILL’ S EQUATION. Journal of Universal Mathematics 7 To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI" 23–30.
IEEE E. Başkaya, “ON SOME ASYMPTOTIC EIGENVALUES OF HILL’ S EQUATION”, JUM, vol. 7, no. To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI", pp. 23–30, 2024, doi: 10.33773/jum.1557752.
ISNAD Başkaya, Elif. “ON SOME ASYMPTOTIC EIGENVALUES OF HILL’ S EQUATION”. Journal of Universal Mathematics 7/To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI" (December 2024), 23-30. https://doi.org/10.33773/jum.1557752.
JAMA Başkaya E. ON SOME ASYMPTOTIC EIGENVALUES OF HILL’ S EQUATION. JUM. 2024;7:23–30.
MLA Başkaya, Elif. “ON SOME ASYMPTOTIC EIGENVALUES OF HILL’ S EQUATION”. Journal of Universal Mathematics, vol. 7, no. To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI", 2024, pp. 23-30, doi:10.33773/jum.1557752.
Vancouver Başkaya E. ON SOME ASYMPTOTIC EIGENVALUES OF HILL’ S EQUATION. JUM. 2024;7(To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI"):23-30.