References
- Borg G. Eine Umkehrung der Sturm–Liouvilleschen Eigenwertaufgabe. Acta Math. 1946;78:1–96. doi: 10.1007/BF02421600
- Gasymov MG, Levitan BM. The inverse problem for the Dirac system. Dokl Akad Nauk SSSR. 1966;167(5):967–970.
- Gasymov MG, Dzabiev TT. Solution of the inverse problem by two spectra for the Dirac equation on a finite interval. Akad Nauk Azerbaijan SSR Dokl. 1966;22(7):3–6.
- Marchenko VA. Sturm–Liouville operators and their applications. Kiev: Naukova Dumka; 1977. English transl., Birkhäuser, 1986.
- Levitan BM, Sargsyan IS. Sturm–Liouville and Dirac operators. Moscow: Nauka; 1988. English transl., Kluwer Academic Publishers, Dordrecht, 1991.
- Malamud MM. Uniqueness questions in inverse problems for systems of differential equations on a finite interval. Trans Moscow Math Soc. 1999;60:204–262.
- Freiling G, Yurko VA. Inverse Sturm–Liouville problems and their applications. New York: NOVA Science Publishers; 2001.
- Yang CF, Huang ZY. Reconstruction of the Dirac operator from nodal data. Integr Eqns Oper Theory. 2010;66:539–551. doi: 10.1007/s00020-010-1763-1
- Yang CF. Hochstadt–Lieberman theorem for Dirac operator with eigenparameter dependent boundary conditions. Nonlinear Anal. 2011;74:2475–2484. doi: 10.1016/j.na.2010.12.003
- Mykytyuk YV, Puyda DV. Inverse spectral problems for Dirac operators on a finite interval. J Math Anal Appl. 2012;386:177–194. doi: 10.1016/j.jmaa.2011.07.061
- Gorbunov OB, Yurko VA. Inverse problem for Dirac system with singularities in interior points. Anal Math Phys. 2016;6:1–29. doi: 10.1007/s13324-015-0097-1
- Wang YP, Yurko VA. On the missing eigenvalue problem for Dirac operators. Appl Math Lett. 2018;80:41–47. doi: 10.1016/j.aml.2018.01.004
- Yurko VA. Method of spectral mappings in the inverse problem theory. Utrecht: VSP; 2002. (Inverse and Ill-posed Problems Series).
- Beals R, Deift P, Tomei C. Direct and inverse scattering on the line. Providence (RI): AMS; 1988. (Mathematical Surveys and Monographs, 28).
- Yurko VA. Inverse spectral problems for differential operators and their applications. Amsterdam: Gordon and Breach Science Publishers; 2000.
- Yurko VA. An inverse spectral problem for singular non-selfadjoint differential systems. Matem Sbornik. 2004;195(12):123–156. English transl. in Sbornik: Mathematics. 2004;195(12):1823–1854. doi: 10.4213/sm869
- Yurko VA. Inverse spectral problems for differential systems on a finite interval. Results Math. 2005;48(3–4):371–386. doi: 10.1007/BF03323374
- Yurko VA. An inverse problem for differential systems on a finite interval in the case of multiple roots of the characteristic polynomial. Diff. Uravn. 2005;41(6):781–786. English transl. in Diff. Eqns. 2005;41(6):818–823.
- Yurko VA. An inverse problem for differential systems with multiplied roots of the characteristic polynomial. J Inv Ill-Posed Probl. 2005;13(5):503–512. doi: 10.1515/156939405775297425
- Lakshmikantham V, Rama Mohana Rao M. Theory of integro-differential equations, Stability and Control: Theory, Methods and Applications, v.1, Gordon and Breach Science Publishers, Singapore, 1995.
- Malamud MM. On some inverse problems. Kiev: Boundary Value Problems of Mathematical Physics; 1979; p. 116–124.
- Yurko VA. Inverse problem for integro-differential operators of the first order. Funct Anal Ul'janovsk. 1984;22:144–151.
- Eremin MS. An inverse problem for a second-order integro-differential equation with a singularity. Diff Uravn. 1988;24(2):350–351.
- Yurko VA. An inverse problem for integro-differential operators. Mat Zametki. 1991;50(5):134–146. (Russian); English transl. in Math. Notes 1991;50(5–6):1188–1197.
- Buterin SA. On an inverse spectral problem for a convolution integro-differential operator. Results Math. 2007;50(34):173–181. doi: 10.1007/s00025-007-0244-6
- Kuryshova Ju V. Inverse spectral problem for integro-differential operators. Mat Zametki. 2007;81(6):855–866. (Russian); English transl. in Math. Notes 2007;81(6):767–777. doi: 10.4213/mzm3736
- Buterin SA. On the reconstruction of a convolution perturbation of the Sturm–Liouville operator from the spectrum. Diff Uravn. 2010;46:146–149. (Russian); English transl. in Diff. Eqns. 2010;46:150–154.
- Kuryshova Yu V, Shieh C-T. An inverse nodal problem for integro-differential operators. J Inverse Ill-Posed Prob. 2010;18(4):357–369.
- Wang Y, Wei G. The uniqueness for Sturm–Liouville problems with aftereffect. Acta Math Sci. 2012;32A(6):1171–1178.
- Yurko VA. An inverse spectral problems for integro-differential operators. Far East J Math Sci. 2014;92(2):247–261.
- Buterin SA, Choque Rivero AE. On inverse problem for a convolution integro-differential operator with Robin boundary conditions. Appl Math Lett. 2015;48:150–155. doi: 10.1016/j.aml.2015.04.003
- Buterin SA, Sat M. On the half inverse spectral problem for an integro-differential operator. Inverse Probl Sci Eng. 2017;25(10):1508–1518. doi: 10.1080/17415977.2016.1267171
- Yurko VA. Inverse problems for second order integro-differential operators. Appl Math Lett. 2017;74:1–6. doi: 10.1016/j.aml.2017.04.013
- Buterin SA. On inverse spectral problems for first-order integro-differential operators with discontinuities. Appl Math Lett. 2018;78:65–71. doi: 10.1016/j.aml.2017.11.005
- Bondarenko NP. An inverse problem for an integro-differential operator on a star-shaped graph. Math Meth Appl Sci. 2018;41(4):1697–1702. doi: 10.1002/mma.4698
- Ignatyev M. On an inverse spectral problem for the convolution integro-differential operator of fractional order. Results Math. 2018;73:34. DOI:10.1007/s00025-018-0800-2
- Bondarenko N, Buterin S. On recovering the Dirac operator with an integral delay from the spectrum. Results Math. 2017;71(3–4):1521–1529. doi: 10.1007/s00025-016-0568-1
- Bondarenko NP. Inverse problem for the Dirac system with an integral delay of the convolution-type, in: Mathematika. Mekhanika, Vol. 19, Saratov Univ., Saratov, 2017, 9–12.
- Bondarenko NP. An inverse problem for the integro-differential Dirac system with partial information given on the convolution kernel. J Inverse Ill-Pose P. 2018. DOI:10.1515/jiip-2017-0058
- Buterin SA. The inverse problem of recovering the Volterra convolution operator from the incomplete spectrum of its rank-one perturbation. Inverse Probl. 2006;22:2223–2236. doi: 10.1088/0266-5611/22/6/019
- Buterin S, Malyugina M. On global solvability and uniform stability of one nonlinear integral equation. Results Math. 2018. DOI:10.1007/s00025-018-0879-5