Abstract
Non-self-adjoint second-order differential operators with a constant delay are studied. Properties of spectral characteristics are established and the inverse problem of recovering operators from their spectra is investigated. For this nonlinear inverse problem an algorithm for constructing the global solution is developed.
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Bondarenko, N.P., Yurko, V.A.: An inverse problem for Sturm-Liouville differential operators with deviating argument. Appl. Math. Lett. 83, 140–144 (2018)
Buterin, S.A., Yurko, V.A.: An inverse spectral problem for Sturm-Liouville operators with a large constant delay. Anal. Math. Phys. (2017). https://doi.org/10.1007/s13324-017-0176-6
Freiling, G., Yurko, V.A.: Inverse Sturm-Liouville Problems and Their Applications. NOVA Science Publishers, New York (2001)
Freiling, G., Yurko, V.A.: Inverse problems for Sturm-Liouville differential operators with a constant delay. Appl. Math. Lett. 25, 1999–2004 (2012)
Hale, J.: Theory of Functional-Differential Equations. Springer, New York (1977)
Levitan, B.M.: Inverse Sturm-Liouville Problems, Nauka, Moscow, 1984; Engl. transl., VNU Sci.Press, Utrecht, (1987)
Marchenko, V.A.: Sturm-Liouville Operators and Their Applications, Naukova Dumka, Kiev, 1977. English transl, Birkhäuser (1986)
Myshkis, A.D.: Linear Differential Equations with a Delay Argument. Nauka, Moscow (1972)
Vladičić, V., Pikula, M.: An inverse problem for Sturm-Liouville-type differential equation with a constant delay. Sarajevo J. Math. 12(24), 83–88 (2016)
Yang, C.-F.: Trace and inverse problem of a discontinuous Sturm-Liouville operator with retarded argument. J. Math. Anal. Appl. 395(1), 30–41 (2012)
Yurko, V.A.: Method of Spectral Mappings in the Inverse Problem Theory. Inverse and Ill-posed Problems Series, VSP, Utrecht (2002)
Acknowledgements
This work was supported in part by Grant 1.1660.2017/4.6 of the Russian Ministry of Education and Science and by Grant 19-01-00102 of Russian Foundation for Basic Research.
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Yurko, V. An Inverse Spectral Problem for Second Order Differential Operators with Retarded Argument. Results Math 74, 71 (2019). https://doi.org/10.1007/s00025-019-0999-6
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DOI: https://doi.org/10.1007/s00025-019-0999-6