ON SOME ASYMPTOTIC EIGENVALUES OF HILL' S EQUATION

Yıl 2024, Cilt: 7 Sayı: To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI", 23 - 30, 29.12.2024

Elif Başkaya

https://doi.org/10.33773/jum.1557752

Öz

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.

Anahtar Kelimeler

Asymptotic Eigenvalues, Hill, Symmetric Potential

Kaynakça

• 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).