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 Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 7, Pages 1202–1208 (Mi zvmmf4560)

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

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

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

Abstract: Certain properties of the nonlinear self-adjoint eigenvalue problem for Hamiltonian systems of ordinary differential equations with singularities are examined. Under certain assumptions on the way in which the matrix of the system and the matrix specifying the boundary condition at a regular point depend on the spectral parameter, a numerical method is proposed for determining the number of eigenvalues lying on a prescribed interval of the spectral parameter.

Key words: Hamiltonian system of ordinary differential equations, nonlinear eigenvalue problem, eigenvalue, numerical method for determining the number of eigenvalues.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:7, 1133–1139

Bibliographic databases:

UDC: 519.624.1

Citation: A. A. Abramov, V. I. Ul'yanova, L. F. Yukhno, “On the self-adjoint nonlinear eigenvalue problem for Hamiltonian systems of ordinary differential equations with singularities”, Zh. Vychisl. Mat. Mat. Fiz., 48:7 (2008), 1202–1208; Comput. Math. Math. Phys., 48:7 (2008), 1133–1139

Citation in format AMSBIB
\Bibitem{AbrUlyYuk08} \by A.~A.~Abramov, V.~I.~Ul'yanova, L.~F.~Yukhno \paper On the self-adjoint nonlinear eigenvalue problem for Hamiltonian systems of ordinary differential equations with singularities \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2008 \vol 48 \issue 7 \pages 1202--1208 \mathnet{http://mi.mathnet.ru/zvmmf4560} \transl \jour Comput. Math. Math. Phys. \yr 2008 \vol 48 \issue 7 \pages 1133--1139 \crossref{https://doi.org/10.1134/S0965542508070063} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000262334500006} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-47849122933} 

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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 the general nonlinear selfadjoint spectral problem for systems of ordinary differential equations with singularities”, Comput. Math. Math. Phys., 50:1 (2010), 32–37
2. 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
3. Abramov A.A., Ul'yanova V.I., Yukhno L.F., “Determination of the number of an eigenvalue of a singular nonlinear self-adjoint spectral problem for a linear Hamiltonian system of differential equations”, Differ. Equ., 47:8 (2011), 1110–1115
4. A. A. Abramov, L. F. Yukhno, “A nonlinear singular eigenvalue problem for a Hamiltonian system of differential equations with redundant condition”, Comput. Math. Math. Phys., 55:4 (2015), 597–606
5. Abramov A.A. Yukhno L.F., “Nonlinear Spectral Problem For a Self-Adjoint Vector Differential Equation”, Differ. Equ., 53:7 (2017), 900–907
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