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Izv. Akad. Nauk SSSR Ser. Mat., 1972, Volume 36, Issue 2, Pages 450–471 (Mi izv2305)  

This article is cited in 5 scientific papers (total in 5 papers)

Normal solvability of linear differential equations in the complex plane

Yu. F. Korobeinik


Abstract: The operator $L_nY=A(z)Y'(z)+B(z)Y(z)$, where $A(z)$ and $B(z)$ are square $n$th order matrices, regular in a region $G$ of arbitrary connectivity, and $Y(z)$ is a single-column matrix, regular in $G$, is investigated. The operator $L_nY$ is shown to be normally solvable in the space $A^n(G)$ of single-column matrices regular in $G$, and in certain subspaces of $A^n(G)$, and its index is evaluated.

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English version:
Mathematics of the USSR-Izvestiya, 1972, 6:2, 445–466

Bibliographic databases:

UDC: 517.9
MSC: Primary 34A20; Secondary 34A30
Received: 31.05.1971

Citation: Yu. F. Korobeinik, “Normal solvability of linear differential equations in the complex plane”, Izv. Akad. Nauk SSSR Ser. Mat., 36:2 (1972), 450–471; Math. USSR-Izv., 6:2 (1972), 445–466

Citation in format AMSBIB
\Bibitem{Kor72}
\by Yu.~F.~Korobeinik
\paper Normal solvability of linear differential equations in the complex plane
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1972
\vol 36
\issue 2
\pages 450--471
\mathnet{http://mi.mathnet.ru/izv2305}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=301566}
\zmath{https://zbmath.org/?q=an:0259.34073}
\transl
\jour Math. USSR-Izv.
\yr 1972
\vol 6
\issue 2
\pages 445--466
\crossref{https://doi.org/10.1070/IM1972v006n02ABEH001882}


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    Remarks

    This publication is cited in the following articles:
    1. L.J Grimm, L.M Hall, “An alternative theorem for singular differential systems”, Journal of Differential Equations, 18:2 (1975), 411  crossref
    2. S. G. Merzlyakov, “Perturbations of linear operators in spaces of holomorphic functions”, Sb. Math., 186:3 (1995), 409–434  mathnet  crossref  mathscinet  zmath  isi
    3. L.J. Grimm, B.D. Haile, L.M. HALL, “Families of regular solutions of singular systems”, Journal of Difference Equations and Applications, 7:1 (2001), 51  crossref
    4. W.J. Fitzpatrick, L.J. Grimm, L.M. Hall, “Difference Equations and Lettenmeyer's Theorem”, Journal of Difference Equations and Applications, 8:11 (2002), 1053  crossref
    5. Yu. F. Korobeinik, “O primenenii teorii vozmuschenii normalno razreshimykh operatorov k nekotorym klassam operatorov v kompleksnoi oblasti”, Vladikavk. matem. zhurn., 7:2 (2005), 64–77  mathnet  mathscinet  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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