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Associated functions of a nonlinear spectral problem for a system of ordinary differential equations

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Abstract

We study the notion of associated functions of a nonlinear spectral problem for a linear system of ordinary differential equations supplemented with nonlocal conditions given by a Stieltjes integral. We establish the relationship of this problem with the corresponding problem in a finite-dimensional linear space. We consider a numerical method for finding associated functions and justify its stability.

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References

  1. Faddeev, D.K. and Faddeeva, V.N., Vychislitel’nye metody lineinoi algebry (Computational Methods of Linear Algebra), St. Petersburg, 2002.

    Google Scholar 

  2. Keldysh, M.V., On the Characteristic Values and Characteristic Functions of Certain Classes of Nonself-Adjoint Equations, Dokl. Akad. Nauk SSSR, 1951, vol. 77, pp. 11–14.

    Google Scholar 

  3. Keldysh, M.V., The Completeness of Eigenfunctions of Certain Classes of Nonself-Adjoint Linear Operators, Uspekhi Mat. Nauk, 1971, vol. 26, no. 4 (160), pp. 15–41.

    MATH  Google Scholar 

  4. Naimark, M.A., Lineinye differentsial’nye operatory (Linear Differential Operators), Moscow: Fizmatlit, 2010.

    Google Scholar 

  5. Keldysh, M.V. and Lidskii, V.B., On the Spectral Theory of Nonself-Adjoint Operators, Tr. IV vsesoyuz. mat. s’ezda (Proc. Fourth All-Union Math. Congr. (Leningrad, 1961), Leningrad: Izdat. Akad. Nauk SSSR, 1963, vol. 1, pp. 101–120.

    Google Scholar 

  6. Abramov, A.A. and Yukhno, L.F., Root Vectors of Nonlinear Finite-Dimensional Spectral Problem, Zh. Vychisl. Mat. Mat. Fiz., 2016, vol. 56, no. 2, pp. 187–192.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Dorodnitsyn Computing Center, Russian Academy of Sciences, Moscow, Russia

    A. A. Abramov & L. F. Yukhno

  2. Keldysh Institute of Applied Mathematics, Moscow, Russia

    A. A. Abramov & L. F. Yukhno

  3. National Research Nuclear University MEPHI, Moscow, Russia

    A. A. Abramov & L. F. Yukhno

Authors
  1. A. A. Abramov
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  2. L. F. Yukhno
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Corresponding author

Correspondence to A. A. Abramov.

Additional information

Original Russian Text © A.A. Abramov, L.F. Yukhno, 2016, published in Differentsial’nye Uravneniya, 2016, Vol. 52, No. 7, pp. 878–886.

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Abramov, A.A., Yukhno, L.F. Associated functions of a nonlinear spectral problem for a system of ordinary differential equations. Diff Equat 52, 836–844 (2016). https://doi.org/10.1134/S001226611607003X

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  • DOI: https://doi.org/10.1134/S001226611607003X

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