Spectral properties of boundary-value-transmission problems with a constant retarded argument
Spectral properties of boundary-value-transmission problems with a constant retarded argument
In this work, spectra and asymptotics of eigenfunctions of a generalized class of boundary value problemswith constant retarded argument are obtained. Contrary to previous works in the literature, the problem has nonclassicaltransmission conditions.
___
- [1] Akgun FA, Bayramov A, Bayramoğlu M. Discontinuous boundary value problems with retarded argument and
eigenparameter-dependent boundary conditions. Mediterr J Math 2013; 10: 277-288.
- [2] Aydemir K, Mukhtarov OS. Asymptotic distribution of eigenvalues and eigenfunctions for a multi-point discontinuous
Sturm-Liouville problem. Electron J Differential Equations 2016; 131: 1-14.
- [3] Aydemir K, Mukhtarov OS. Class of Sturm-Liouville problems with eigenparameter dependent transmission conditions.
Numer Funct Anal Optim 2017; 38: 1260-1275.
- [4] Bayramov A, C̣alıṣkan S, Uslu S. Computation of eigenvalues and eigenfunctions of a discontinuous boundary value
problem with retarded argument. Appl Math Comput 2007; 191: 592-600.
- [5] Buterin SA, Pikula M, Yurko VA. Sturm-Liouville differential operators with deviating argument. Tamkang J Math
2017; 48: 61-71.
- [6] Fulton CT. Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions.
Proc Roy Soc Edinburgh, A 1977; 77: 293-308.
- [7] Kamenskii GA. On the asymptotic behaviour of solutions of linear differential equations of the second order with
retarded argument. Uch Zap Mosk Gos Univ 1954; 165: 195-204 (in Russian).
- [8] Levitan BM. Expansion in Characteristic Functions of Differential Equations of the Second Order. Moscow, USSR:
GITTL, 1950 (in Russian).
- [9] Mukhtarov OS, Kadakal M, Muhtarov FS. On discontinuous Sturm-Liouville problems with transmission conditions.
J Math Kyoto Univ 2004; 44: 779-798.
- [10] Norkin SB. On boundary problem of Sturm-Liouville type for second-order differential equation with retarded
argument. Izv Vysś Ućebn Zaved Matematika 1958; 6: 203-214 (in Russian).
- [11] Norkin SB. Differential Equations of the Second Order with Retarded Argument. Translations of Mathematical
Monographs, Vol. 31. Providence, RI, USA: AMS, 1972.
- [12] Pikula M, Vladicic V, Markovic O. A solution to the inverse problem for the Sturm-Liouville-type equation with a
delay. Filomat 2013; 27: 1237-1245.
- [13] Ronto NI. Convergence of the method of trigonometric collocation for nonlinear periodic systems of differential
equations with retarded argument. Ukrainian Math J 1983; 35: 692-696.
- [14] Şen E. Sturm-Liouville problems with retarded argument and a finite number of transmission conditions. Electron
J Differential Equations 2017; 310: 1-8.
- [15] Şen E, Acikgoz M, Araci S. Spectral problem for the Sturm–Liouville operator with retarded argument containing
a spectral parameter in the boundary condition. Ukrainian Math J 2017; 8: 1263-1277.
- [16] Şen E, Bayramov A. Calculation of eigenvalues and eigenfunctions of a discontinuous boundary value problem with
retarded argument which contains a spectral parameter in the boundary condition. Math Comput Model 2011; 54:
3090-3097.
- [17] Titchmarsh EC. Eigenfunctions Expansion Associated with Second Order Differential Equation, Part 1. 2nd ed.
Oxford, UK: Oxford University Press, 1962.
- [18] Yang CF. Inverse nodal problems for the Sturm–Liouville operator with a constant delay. J Differential Equations
2014; 257: 1288-1306.
- [19] Yurko V. Inverse spectral problems for Sturm-Liouville operators with complex weights. Inverse Probl Sci Eng 2018;
26: 1396-1403.