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On the general nonlinear self-adjoint eigenvalue problem for systems of ordinary differential equations with singularities

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Abstract

A nonlinear self-adjoint eigenvalue problem for the general linear system of ordinary differential equations is examined on an unbounded interval. A method is proposed for the approximate reduction of this problem to the corresponding problem on a finite interval. Under the assumption that the initial data are monotone functions of the spectral parameter, a method is given for determining the number of eigenvalues lying on a prescribed interval of this parameter. No direct calculation of eigenvalues is required in this method.

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References

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Authors and Affiliations

  1. Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

    A. A. Abramov & V. I. Ul’yanova

  2. Institute of Mathematical Modeling, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia

    L. F. Yukhno

Authors
  1. A. A. Abramov
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  2. V. I. Ul’yanova
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  3. L. F. Yukhno
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Correspondence to A. A. Abramov.

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Original Russian Text © A.A. Abramov, V.I. Ul’yanova, L.F. Yukhno, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 1, pp. 38–43.

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Abramov, A.A., Ul’yanova, V.I. & Yukhno, L.F. On the general nonlinear self-adjoint eigenvalue problem for systems of ordinary differential equations with singularities. Comput. Math. and Math. Phys. 50, 32–37 (2010). https://doi.org/10.1134/S0965542510010057

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  • DOI: https://doi.org/10.1134/S0965542510010057

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