A Boundary Value Problem with Retarded Argument Containing an Eigenparameter in the Transmission Condition

Year 2023, Volume: 9 Issue: 2, 282 - 288, 31.12.2023

Özge Işık Gülmezler Özgür Mızrak

https://doi.org/10.29132/ijpas.1368045

Abstract

In this work, a discontinuous boundary value problem with retarded argument is studied. At the discontinuity point there is a transmission condition that contains a parameter. Asymptotic properties of eigenvalues and corresponding eigenfunctions of the boundary value problem are studied.

Keywords

retarded argument, eigenvalue, eigenfunction, transmission condition

References

• Aydin Akgun, F., Bayramov, A. and Bayramoğlu, M. (2013). Discontinuous boundary value problems with retarded argument and eigenparameter-dependent boundary conditions. Mediterranean journal of mathematics, 10(1), 277-288.
• Bayramoğlu, M., Köklü, K. Ö. and Baykal, O. (2002). On the spectral properties of the regular Sturm-Liouville Problem with the lag argument for which its boundary conditions depends on the spectral parameter. Turkish Journal of Mathematics, 26(4), 421-432.
• Cetinkaya, F. A. and Mamedov, K. R. (2017). A boundary value problem with retarded argument and discontinuous coefficient in the differential equation. Azerbaijan Journal of Mathematics, 7(1), 135-145.
• Hira, F. (2017). A trace formula for the Sturm-Liouville type equation with retarded argument. Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat, 66(1), 124-132.
• Kolmanovskii, V. and Myshkis, A. (1999). Introduction to the Theory and Applications of Functional Differential Equations. Dordrecht, The Nederlands: Kluwer Academic Publishers.
• Koparan, K. (2019). Sınırda parametre içeren geç kalan argümanlı Sturm Liouville probleminin özdeğerlerinin ve özfonksiyonlarının asimtotik özellikleri, Yüksek Lisans Tezi.
• Norkin, S. B. (1956). Boundary problem for a secondorder differential equation with a retarded argument. Uchenye Zapiski Moskovskogo Gosudarstvennogo Universiteta, 181, 59-72.
• Norkin, S. B. (1958). On periodic solutions of a linear homogeneous differential equation of second order with retarded argument. Matematicheskii Sbornik, 87(1), 71-104.
• Norkin, S. B. (1972). Differential Equations of the Second Order with Retarded Argument, Providence, Rhode Island: American Mathematical Society.
• Şen, E. and Bayramov, A. (2011). On calculation of eigenvalues and eigenfunctions of a Sturm-Liouville type problem with retarded argument which contains a spectral parameter in the boundary condition. Journal of Inequalities and Applications, 2011(1), 1-9.
• Şen, E. and Bayramov, A. (2011). Calculation of eigenvalues and eigenfunctions of a discontinuous boundary value problem with retarded argument which contains a spectral parameter in the boundary condition. Mathematical and Computer Modelling, 54(11-12), 3090-3097.
• Şen, E. and Bayramov, A. (2013). Asymptotic formulations of the eigenvalues and eigenfunctions for a boundary value problem. Mathematical Methods in the Applied Sciences, 36(12), 1512-1519.
• Şen, E., Seo, J. J. and Araci, S. (2013). Asymptotic behaviour of eigenvalues and eigenfunctions of a Sturm-Liouville problem with retarded argument. Journal of Applied Mathematics, 2013.
• Yang, C. F. (2012). Trace and inverse problem of a discontinuous Sturm–Liouville operator with retarded argument. Journal of Mathematical Analysis and Applications, 395(1), 30-41.