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

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

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
Received: 19.10.2007

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
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\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
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\transl
\jour Comput. Math. Math. Phys.
\yr 2008
\vol 48
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\pages 1133--1139
\crossref{https://doi.org/10.1134/S0965542508070063}
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    Citing articles on Google Scholar: Russian citations, English citations
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    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  mathnet  crossref  mathscinet  adsnasa  isi
    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  mathnet  crossref  mathscinet  adsnasa  isi
    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  crossref  mathscinet  zmath  isi  elib  elib  scopus
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. Abramov A.A. Yukhno L.F., “Nonlinear Spectral Problem For a Self-Adjoint Vector Differential Equation”, Differ. Equ., 53:7 (2017), 900–907  crossref  mathscinet  zmath  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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