We investigate a problem for the Dirac differential operators in the case where an eigenparameter not only appears in the differential equation but is also linearly contained in a boundary condition. We prove uniqueness theorems for the inverse spectral problem with known collection of eigenvalues and normalizing constants or two spectra.
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S.-D. Poisson, “Mémoire sur la manière d’exprimer les fuctions par des séries periodiques,” J. École Polytechnique, 11, 417–489 (1820).
C. T. Fulton, “Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions,” Proc. R. Soc. Edinburgh, A, 77, 293–308 (1977).
C. T. Fulton, “Singular eigenvalue problems with eigenvalue parameter contained in the boundary conditions,” Proc. R. Soc. Edinburgh, A, 87, 1–34 (1980).
B. M. Levitan and I. S. Sargsyan, Sturm – Liouville and Dirac Operators [in Russian], Nauka, Moscow (1988).
M. G. Gasymov, “Inverse problem of scattering theory for Dirac system of order 2n,” Tr. Mosk. Mat. Obshch., 19, 41–112 (1968).
I. M. Guseinov, “On representation of Jost solutions of a system of Dirac differential equations with discontinuous coefficients,” Izv. Akad. Nauk Azerb. SSR., No. 5, 41–45 (1999).
R. Kh. Amirov, “On a system of Dirac differential equations with discontinuity conditions inside an interval,” Ukr. Math. J., 57, No. 5, 712–727 (2005).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 9, pp. 1155–1166, September, 2009.
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Amirov, R.K., Keskin, B. & Ozkan, A.S. Direct and inverse problems for the Dirac operator with a spectral parameter linearly contained in a boundary condition. Ukr Math J 61, 1365–1379 (2009). https://doi.org/10.1007/s11253-010-0282-1
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DOI: https://doi.org/10.1007/s11253-010-0282-1