A boundary inverse problem for a second order differential operator.
DOI:
https://doi.org/10.26577/2218-7987-2014-5-2-24-30Keywords:
boundary inverse problem, uniqueness theorem, differential operator, integro–differential boundary condition, spectral analysis, spectrum, eigenfunction, associated function, basis, conjugate system, biorthogonal systemAbstract
In this paper we investigate a boundary inverse problem of a second order differential operator with integral boundary conditions in LReferences
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SSSR Ser. Mat. –1951. –Vol. 15. –№4. –P.309–360.
2. Leibenzon Z. I. The inverse problem of the spectral analysis of ordinary differential operators of higher orders (Russian) // Tr. Mosk. Mat. Obs. –1966. –Vol. 15. –P. 70–144.Yurko V. A. The inverse problem for
differential operators of second order with regular boundary conditions (Russian) // Mat. Zametki.–1975. –Vol.18. –№4. –P. 569–576.
4. Marchenko V. A. Introduction to the theory of inverse problems of spectral analysis (Russian). –Akta: Kharkiv, 2005. –324p.
5. Sadovnichy V. A. Uniqueness theorem for the inverse problem of spectral analysis in the case of differential equations with periodic boundary conditions (Russian) // Differents. Uravn. –1973. –Vol. 9. –№2. –P. 271–277.
6. Sadovnichy V. A., Kanguzhin B. E. On the connection between the spectrum of a differential operator with symmetric coefficients and boundary conditions (Russian) // Dokl. Akad. Nauk SSSR. –1982. –Vol. 267. –№2. –P. 310–313.
7. Akhtyamov A. M., Sadovnichy V. A., Sultanaev Ya. T. Generalizations of Borg’s uniqueness theorem to the case of nonseparated
boundary conditions // Eurasian Math. J. –2012. –Vol. 3. –№4. –P. 10–22.
8. Akhtyamov A. M., Sadovnichy V. A., Sultanaev Ya. T. Inverse problem for an operator
pencil with nonseparated boundary conditions // Eurasian Math. J. –2010. –Vol. 1. –№2. –P. 5–16.
9. Shkalikov A. A. Basis property of eigenfunctions of ordinary differential operators with integral boundary conditions (Russian) //
Vestnik Moskov. Univ. Ser. I Mat. Mekh. –1982.–№6 . –P. 12–21.
10. Bari N. K. Biorthogonal systems and bases in Hilbert space (Russian) // Uch. Zap. Mosk. Gos.Univ. –1951. –Vol. 148. –P. 69–107.
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Kanguzhin, B., & Tokmagambetov, N. (2014). A boundary inverse problem for a second order differential operator. International Journal of Mathematics and Physics, 5(2), 24–30. https://doi.org/10.26577/2218-7987-2014-5-2-24-30
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Algebra and Mathematical Analysis
