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An Inverse Spectral Problem for Second Order Differential Operators with Retarded Argument

  • V. YurkoEmail author
Article
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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.

Keywords

Differential operators retarded argument inverse spectral problems 

Mathematics Subject Classification

34A55 34K10 34K29 47E05 34B10 34L40 

Notes

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.

References

  1. 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)MathSciNetCrossRefGoogle Scholar
  2. 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 CrossRefGoogle Scholar
  3. 3.
    Freiling, G., Yurko, V.A.: Inverse Sturm-Liouville Problems and Their Applications. NOVA Science Publishers, New York (2001)zbMATHGoogle Scholar
  4. 4.
    Freiling, G., Yurko, V.A.: Inverse problems for Sturm-Liouville differential operators with a constant delay. Appl. Math. Lett. 25, 1999–2004 (2012)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Hale, J.: Theory of Functional-Differential Equations. Springer, New York (1977)CrossRefGoogle Scholar
  6. 6.
    Levitan, B.M.: Inverse Sturm-Liouville Problems, Nauka, Moscow, 1984; Engl. transl., VNU Sci.Press, Utrecht, (1987)Google Scholar
  7. 7.
    Marchenko, V.A.: Sturm-Liouville Operators and Their Applications, Naukova Dumka, Kiev, 1977. English transl, Birkhäuser (1986)Google Scholar
  8. 8.
    Myshkis, A.D.: Linear Differential Equations with a Delay Argument. Nauka, Moscow (1972)Google Scholar
  9. 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)MathSciNetGoogle Scholar
  10. 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)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Yurko, V.A.: Method of Spectral Mappings in the Inverse Problem Theory. Inverse and Ill-posed Problems Series, VSP, Utrecht (2002)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsSaratov State UniversitySaratovRussia

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