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An inverse spectral problem for second order differential operators with retarded argument. (English) Zbl 1465.34085

Non-self-adjoint second-order differential operators with a constant delay are studied. The following results are provided: (1) properties of spectral characteristics are established; (2) the inverse problem of recovering operators from their spectra is investigated; (3) for this nonlinear inverse problem an algorithm for constructing the global solution is developed. The results are meaningful and valuable.

MSC:

34K29 Inverse problems for functional-differential equations
34K10 Boundary value problems for functional-differential equations
47E05 General theory of ordinary differential operators
34K08 Spectral theory of functional-differential operators
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[1] Bondarenko, N.P., Yurko, V.A.: An inverse problem for Sturm-Liouville differential operators with deviating argument. Appl. Math. Lett. 83, 140-144 (2018) · Zbl 1489.34105 · doi:10.1016/j.aml.2018.03.025
[2] 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 · doi:10.1007/s13324-017-0176-6
[3] Freiling, G., Yurko, V.A.: Inverse Sturm-Liouville Problems and Their Applications. NOVA Science Publishers, New York (2001) · Zbl 1037.34005
[4] Freiling, G., Yurko, V.A.: Inverse problems for Sturm-Liouville differential operators with a constant delay. Appl. Math. Lett. 25, 1999-2004 (2012) · Zbl 1257.34056 · doi:10.1016/j.aml.2012.03.026
[5] Hale, J.: Theory of Functional-Differential Equations. Springer, New York (1977) · doi:10.1007/978-1-4612-9892-2
[6] Levitan, B.M.: Inverse Sturm-Liouville Problems, Nauka, Moscow, 1984; Engl. transl., VNU Sci.Press, Utrecht, (1987) · Zbl 0575.34001
[7] Marchenko, V.A.: Sturm-Liouville Operators and Their Applications, Naukova Dumka, Kiev, 1977. English transl, Birkhäuser (1986) · Zbl 0399.34022
[8] Myshkis, A.D.: Linear Differential Equations with a Delay Argument. Nauka, Moscow (1972)
[9] 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) · Zbl 1424.34264
[10] 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) · Zbl 1255.34065 · doi:10.1016/j.jmaa.2012.04.078
[11] Yurko, V.A.: Method of Spectral Mappings in the Inverse Problem Theory. Inverse and Ill-posed Problems Series, VSP, Utrecht (2002) · Zbl 1098.34008
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