Inverse problem for Sturm–Liouville differential operators with two constant delays
Inverse problem for Sturm–Liouville differential operators with two constant delays
In this manuscript, we study nonself-adjoint second-order differential operators with two constant delays.We investigate the properties of the spectral characteristics and the inverse problem of recovering operators from theirspectra. An inverse spectral problem is studied of recovering the potential from spectra of two boundary value problemswith one common boundary condition. The uniqueness theorem is proved for this inverse problem.
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- 1] Bondarenko N, Yurko VA. On recovering Sturm-Liouville differential operators with deviating argument. 2018
arXiv preprint, arXiv:1802.02321.
- [2] Borg G. Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Acta Mathematica 1945; 78: 1-96 (in
German).
- [3] Buterin SA, Pikula M, Yurko VA. Sturm-Liouville differential operators with deviating argument. Tamkang Journal
of Mathematics 2017; 48 (1): 61-71.
- [4] Buterin SA, Yurko VA. An inverse spectral problem for Sturm–Liouville operators with a large constant delay.
Analysis and Mathematical Physics 2017; 71 (3): 1521–1529. doi: 10.1007/s13324-017-0176-6
- [5] Conway JB. Functions of One Complex Variable, Vol. 1. 2nd ed. New York, NY, USA: Springer-Verlag, 1995.
- [6] Freiling G, Yurko VA. Inverse Sturm–Liouville Problems and Their Applications. New York, NY, USA: NOVA
Science Publishers, 2001.
- [7] Freiling G, Yurko VA. Inverse problems for Sturm–Liouville differential operators with a constant delay. Applied
Mathematics Letters 2012; 25: 1999-2004.
- [8] Hale J. Theory of Functional-Differential Equations. New York, NY, USA: Springer-Verlag, 1977.
- [9] Levitan BM. Inverse Sturm-Liouville Problems. Utrecht, the Netherlands: VNU Science Press, 1987.
- [10] Mosazadeh S. On the solution of an inverse Sturm–Liouville problem with a delay and eigenparameter-dependent
boundary conditions. Turkish Journal of Mathematics 2018; 42: 3090-3100.
- [11] Mosazadeh S, Jodayree Akbarfam A. On Hochstadt–Lieberman theorem for impulsive Sturm–Liouville problems
with boundary conditions polynomially dependent on the spectral parameter. Turkish Journal of Mathematics 2018;
42: 3002-3009.
- [12] Myshkis AD. Linear Differential Equations with a Delay Argument. Moscow, USSR: Nauka, 1972 (in Russian).
- [13] Norkin SB. Second Order Differential Equations with a Delay Argument. Moscow, USSR: Nauka, 1965 (in Russian).
- [14] Pikula M. Determination of a Sturm–Liouville-type differential operator with delay argument from two spectra.
Matematicki Vesnik 1991; 43 (3-4): 159-171.
- [15] Pikula M, Vladicic V, Markovic O. A solution to the inverse problem for the Sturm–Liouville-type equation with
a delay. Filomat 2013; 27 (7): 1237-1245.
- [16] Smith H. An Introduction to Delay Differential Equations with Sciences Applications to the Life. New York, NY,
USA: Springer, 2011.
- [17] Teschl G. Mathematical Methods in Quantum Mechanics, with Applications to Schrödinger Operators. Graduate
Studies in Mathematics. Providence, RI, USA: American Mathematical Society, 2009.
- [18] Vladicic V, Pikula M. An inverse problems for Sturm–Liouville-type differential equation with a constant delay.
Sarajevo Journals of Mathematics 2016; 12 (24) : 83-88.
- [19] Yang CF. Trace and inverse problem of a discontinuous Sturm–Liouville operator with retarded argument. Journal
of Mathematical Analysis and Applications 2012; 395: 30-41.
- [20] Yurko VA, Yang CF. Recovering differential operators with nonlocal boundary conditions. Analysis and Mathematical
Physics 2016; 6 (4): 315-326.