TY  - JOUR
T1  - On the Eigenvalue Problems with Integrable Potential and Boundary Conditions Rationally Dependent on the Eigenparameter
AU  - Başkaya, Elif
PY  - 2025
DA  - July
Y2  - 2025
JF  - Hitit Journal Of Science
JO  - HJS
PB  - Hitit University
WT  - DergiPark
SN  - 3061-9629
SP  - 37
EP  - 41
VL  - 2
IS  - 2
LA  - en
AB  - 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.
KW  - Boundary Condition Rationally Dependent on the Eigenvalue
KW  - Asymptotic Estimates
KW  - Integrable Potential
CR  - 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.
CR  - 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.
CR  - 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.
CR  - 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.
CR  - 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.
CR  - 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.
CR  - Harris B. J., 1997. The Form of the Spectral Functions Associated with Sturm-Liouville Problems with Continuous Spectrum. Mathematika, 44 (1), 149-161.
CR  - 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.
CR  - Kabataş A., 2022. Eigenfunction and Green’ s function asymptotics for Hill’ s equation with symmetric single-well potential. Ukrainian Mathematical Journal, 74 (2), 218-231.
CR  - Kabataş A., 2023. One boundary value problem including a spectral parameter in all boundary conditions. Opuscula Mathematica, 43 (5), 651-661.
CR  - Kabataş A., 2023. Sturm-Liouville problems with polynomially eigenparameter dependent boundary conditions. Sakarya University Journal of Science, 27 (6), 1235-1242.
CR  - Kabataş A., 2023. Sturm-Liouville problems including boundary conditions polynomially dependent on the eigenparameter with differentiable potential. International Research and Reviews in Science and Mathematics, Serüven Publishing, Ankara, 1-16.
CR  - Kabataş A., 2023. On eigenfunctions of the Sturm-Liouville problems with boundary conditions rationally dependent on the eigenparameter. International Theory, Research and Reviews in Science and Mathematics, Serüven Publishing, Ankara, 263-281.
CR  - Kabataş A., 2023. On Sturm-Liouville problems including the square-root of the eigenvalue parameter in one boundary condition. New Frontiers in Natural Science and Mathematics, Duvar Publishing, İzmir, 233-251.
CR  - Kabataş A., 2024. Green’s function asymptotics for a boundary value problem contained eigenvalue parameter in the boundary condition. Advances in Mathematics Research Volume 35, NOVA Science Publishers Inc. , New York, 43-53.
CR  - Mosazadeh S. and Akbarfam A. J., 2020. Inverse and Expansion Problems with Boundary Conditions Rationally Dependent on the Eigenparameter. Bulletin of the Iranian Mathematical Society, 46, 67-78.
UR  - https://dergipark.org.tr/en/pub/hjs/issue//1710380
L1  - https://dergipark.org.tr/en/download/article-file/4919883
ER  -