Research Article
Year 2023,
Volume: 6 Issue: 3-Supplement, 50 - 57, 15.10.2023
Abstract
References
- S.B. Norkin, Boundary value problem for the diferential equation of the second order with a lagging argument, Uch. app. Moscow State University, 181, Mat-ka, VIII, pp.59-72 (1956).
- S.B. Norkin, On a boundary problem of Sturm-Liouville type for a second-order diferantial equation with a retarded argument, Izv. Vyssh. Uchebn. Zaved. Mat., Vol.6, pp.203-214 (1958).
- E. Sen, A. Bayramov, 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, Vol.54, pp.3090-3097 (2011).
- C. Fu Yang , Trace and inverse problem of a discontinuous Sturm-Liouville operator with retarded argument, J. Math. Anal. Appl., Vol.395, pp.30-41 (2012).
- F. Aydin Akgun, A. Bayramov, M. Bayramoglu, Discontinuous boundary value problems with retarded argument and eigenparameter-dependent boundary conditions, Mediterr. J. Math. Vol.10, pp.277-288 (2013).
- E. Sen, J. Jin Seo, S. Araci, Asymptotic behaviour of eigenvalues and eigenfunctions of a Sturm-Liouville problem with retarded argument, Journal of Applied Mathematics, 306917, (2013).
- M. Bayramoglu, A. Bayramov , E. Sen, A regularized trace formula for a discontinuous Sturm-Liouville operator with delayed argument, Electronic Journal of Diferential Equations, Vol.104, pp.1072-6691 (2017).
- F.A. Cetinkaya , K.R. Mamedov, A boundary value problem with retarded argumant and this continuous coecient in the diferential equation, Azerbaijan Journal of Mathematics, Vol.7, No.1, pp.2218-6816 (2017).
- F. Hira, A trace formula for the Sturm-Liouville type equation with retarded argumnent, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat, Vol.66, No.1, pp.124-132 (2017).
- G. Freiling, V.A. Yurko, Inverse problems for Sturm-Liouville diferantial operators with a constant delay, Applied Mathematics Letters, Vol.25, pp.1999-2004 (2012).
- S. Mosazadeh, On the solution of an inverse Sturm-Liouville problem with a delay and eigenparameter dependent boundary conditions, Turk J Math, Vol.42, pp.3090-3100 (2018).
- N. Bondarenko, V. Yurko, An inverse problem for Sturm{Liouville diferential operators with deviating argument, Appl. Math. Lett. (2018).
- S.B. Norkin, Diferential Equations of the Second Order with Retarded Argument. Providence, Rhode Island: American Mathematical Society, (1972).
BASIC BOUNDARY VALUE PROBLEM WITH RETARDED ARGUMENT CONTAINING AN EIGENPARAMETER IN THE TRANSMISSION CONDITION
Abstract
In this paper basic boundary value problem with retarded argument that has a discontinuity point inside the interval will be studied. At the discontinuity point transmission conditions contain eigenparameter. Existence of eigenvalues and eigenfunctions will be studied. Asmyptotic properties of eigenvalues and eigenfunctions will be obtained.
References
- S.B. Norkin, Boundary value problem for the diferential equation of the second order with a lagging argument, Uch. app. Moscow State University, 181, Mat-ka, VIII, pp.59-72 (1956).
- S.B. Norkin, On a boundary problem of Sturm-Liouville type for a second-order diferantial equation with a retarded argument, Izv. Vyssh. Uchebn. Zaved. Mat., Vol.6, pp.203-214 (1958).
- E. Sen, A. Bayramov, 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, Vol.54, pp.3090-3097 (2011).
- C. Fu Yang , Trace and inverse problem of a discontinuous Sturm-Liouville operator with retarded argument, J. Math. Anal. Appl., Vol.395, pp.30-41 (2012).
- F. Aydin Akgun, A. Bayramov, M. Bayramoglu, Discontinuous boundary value problems with retarded argument and eigenparameter-dependent boundary conditions, Mediterr. J. Math. Vol.10, pp.277-288 (2013).
- E. Sen, J. Jin Seo, S. Araci, Asymptotic behaviour of eigenvalues and eigenfunctions of a Sturm-Liouville problem with retarded argument, Journal of Applied Mathematics, 306917, (2013).
- M. Bayramoglu, A. Bayramov , E. Sen, A regularized trace formula for a discontinuous Sturm-Liouville operator with delayed argument, Electronic Journal of Diferential Equations, Vol.104, pp.1072-6691 (2017).
- F.A. Cetinkaya , K.R. Mamedov, A boundary value problem with retarded argumant and this continuous coecient in the diferential equation, Azerbaijan Journal of Mathematics, Vol.7, No.1, pp.2218-6816 (2017).
- F. Hira, A trace formula for the Sturm-Liouville type equation with retarded argumnent, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat, Vol.66, No.1, pp.124-132 (2017).
- G. Freiling, V.A. Yurko, Inverse problems for Sturm-Liouville diferantial operators with a constant delay, Applied Mathematics Letters, Vol.25, pp.1999-2004 (2012).
- S. Mosazadeh, On the solution of an inverse Sturm-Liouville problem with a delay and eigenparameter dependent boundary conditions, Turk J Math, Vol.42, pp.3090-3100 (2018).
- N. Bondarenko, V. Yurko, An inverse problem for Sturm{Liouville diferential operators with deviating argument, Appl. Math. Lett. (2018).
- S.B. Norkin, Diferential Equations of the Second Order with Retarded Argument. Providence, Rhode Island: American Mathematical Society, (1972).
There are 13 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Ordinary Differential Equations, Difference Equations and Dynamical Systems |
| Journal Section | Research Article |
| Authors | |
| Publication Date | October 15, 2023 |
| Submission Date | September 29, 2023 |
| Acceptance Date | October 12, 2023 |
| Published in Issue | Year 2023 Volume: 6 Issue: 3-Supplement |
