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 Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 1, Pages 38–43 (Mi zvmmf4810)

On the general nonlinear selfadjoint spectral problem for systems of ordinary differential equations with singularities

A. A. Abramova, V. I. Ul'yanovaa, L. F. Yukhnob

a Dorodnitsyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
b Institute of Mathematical Modeling, Russian Academy of Sciences, Miusskaya pl. 4a, Moskow, 125047 Russia

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.

Key words: ordinary differential equation, nonlinear self-adjoint eigenvalue problem, eigenvalues, numerical method for determining the number of eigenvalues.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:1, 32–37

Bibliographic databases:

UDC: 519.62

Citation: A. A. Abramov, V. I. Ul'yanova, L. F. Yukhno, “On the general nonlinear selfadjoint spectral problem for systems of ordinary differential equations with singularities”, Zh. Vychisl. Mat. Mat. Fiz., 50:1 (2010), 38–43; Comput. Math. Math. Phys., 50:1 (2010), 32–37

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. A. Abramov, V. I. Ul'yanova, L. F. Yukhno, “On a singular nonlinear self-adjoint spectral problem for differential-algebraic systems of equations”, Comput. Math. Math. Phys., 50:2 (2010), 238–243
2. M. K. Kerimov, “On the 85th birthday of Aleksandr Aleksandrovich Abramov”, Comput. Math. Math. Phys., 51:10 (2011), 1653–1658
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