Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Yurko V. A. On Inverse Problem for Differential Operators with Deviating Argument. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2018, vol. 18, iss. 3, pp. 328-333. DOI: 10.18500/1816-9791-2018-18-3-328-333, EDN: YBMQLB

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
28.08.2018
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Language: 
English
Heading: 
Mathematics
Article type: 
Article
UDC: 
517.984
DOI: 
10.18500/1816-9791-2018-18-3-328-333
EDN: 
YBMQLB

On Inverse Problem for Differential Operators with Deviating Argument

Autors: 
Yurko Vjacheslav Anatol'evich, Saratov State University
Abstract: 

Second-order functional differential operators with a constant delay are considered. Properties of their spectral characteristics are obtained, and a nonlinear inverse spectral problem is studied, which consists in constructin goperators from the irspectra. We establish the unique nessand develop a constructive procedure for solution of the inverse problem.

Key words: 
differential operators
deviating argument
inverse spectral problem
References: 
  1. Hale J. Theory of functional-differential equations. New York, Springer-Verlag, 1977. 420 p.
  2. Freiling G., Yurko V. Inverse Sturm–Liouville Problems and Their Applications. New York, NOVA Science Publishers, 2001. 305 p.
  3. Yurko V. Method of Spectral Mappings in the Inverse Problem Theory. Inverse and Illposed Problems Series. Utrecht, VSP, 2002. 316 p.
  4. Freiling G., Yurko V. Inverse problems for Sturm–Liouville differential operators with a constant delay. Appl. Math. Lett., 2012, vol. 25, iss. 11, pp. 1999–2004. DOI: https://doi.org/10.1016/j.aml.2012.03.026
  5. Vladiˇ ci´c V., Pikula M. An inverse problem for Sturm–Liouville-type differential equation with a constant delay. Sarajevo J. Math., 2016, vol. 12(24), no. 1, pp. 83–88. DOI: https://doi.org/10.5644/SJM.12.1.06
  6. Yurko V., Buterin S., Pikula M. Sturm–Liouville differential operators with deviating argument. Tamkang J. Math., 2017, vol. 48, no. 1, pp. 61–71. DOI: https://doi.org/10.5556/j.tkjm.48.2017.2264
  7. Buterin S., Yurko V. An inverse spectral problem for Sturm–Liouville operators with a large constant delay. Anal. Math. Phys., 2017, pp. 1–11. DOI: https://doi.org/10.1007/s13324-017-0176-6
Received: 
26.03.2018
Accepted: 
29.07.2018
Published: 
04.09.2018
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