About some properties of degenerate systems of linear integro-differential equations. I
The Bulletin of Irkutsk State University. Series Mathematics, Tome 11 (2015), pp. 13-27 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper contains the linear system integro-differential equations (IDE), with an identically degenerate or rectangular matrix at the derivative of the unknown vector functions, including systems with a weak singularity in the kernel. This paper discusses the structure of the common solutions of such systems.
Keywords: integro-differential equations, index, general solution, singular points.
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N. D. Bang; V. F. Chistyakov; E. V. Chistyakova. About some properties of degenerate systems of linear integro-differential equations. I. The Bulletin of Irkutsk State University. Series Mathematics, Tome 11 (2015), pp. 13-27. http://geodesic.mathdoc.fr/item/IIGUM_2015_11_a1/

[1] Boyarintsev Y. E., Regular and singular systems of linear ordinary differential equations, Nauka, Novosibirsk, 1980

[2] Boyarintsev Y. E., Chistyakov V. F., Algebro-differentsial'nye sistemy. Metody resheniya i issledovaniya, Nauka, Novosibirsk, 1998

[3] Chistyakova E. V., “On a family of singular integro-differential equations”, Computational Mathematics and Mathematical Physics, 51:9, September (2011), 1558–1566 | DOI

[4] Ushakov E. I., Staticheskaia ustoichivost elektricheskikh sistem, Nauka, Novosibirsk, 1988 (in Russian)

[5] Fedorov V. E., Omel'chenko E. A., “Inhomogeneous degenerate Sobolev type equations with delay”, Siberian Mathematical Journal, 53:2, March (2012), 335–344 | DOI

[6] Chistyakov V. F., Algebraic-Differential Operators with Finite-Dimensional Kernel, Nauka, Novosibirsk, 1996

[7] Chistyakova E. V., “Properties of finite-difference schemes for singular integrodifferential equations of index 1”, Computational Mathematics and Mathematical Physics, 49:9, September (2009), 1507–1515 | DOI

[8] Brenan K. E., Numerical solution of initial-value problems in differential-algebraic equations, Classics in applied mathematics, 14, eds. S. L. Campbell, L. R. Petzold, SIAM, Philadelphia, 1996

[9] H. Brunner, Collocation Methods for Volterra Integral and Related Functional Differential Equations, Cambridge University Press, N.Y., 2004

[10] M. V. Falaleev, S. S. Orlov, “Degenerate integro-differential operators in Banach spaces and their applications”, Russian Mathematics, 55:10 (2011), 59–69 | DOI

[11] L. M. Silverman, R. S. Bucy, “Generalizations of theorem of Dolezal”, Math. System Theory, 4 (1970), 334–339 | DOI