Cite this article as:
Yurko V. A. On Inverse Problem for Differential Operators with Deviating Argument. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2018, vol. 18, iss. 3, pp. 328-333. DOI: https://doi.org/10.18500/1816-9791-2018-18-3-328-333
On Inverse Problem for Differential Operators with Deviating Argument
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.
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