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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 6, Pages 999–1002 (Mi zvmmf4575)  

This article is cited in 4 scientific papers (total in 4 papers)

Nonlinear eigenvalue problem for second-order Hamiltonian systems

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, Moscow, 125047, Russia

Abstract: The nonlinear self-adjoint eigenvalue problem for a Hamiltonian system of two ordinary differential equations is examined under the assumption that the matrix of the system is a monotone function of the spectral parameter. Certain properties of eigenvalues that were previously established by the authors for Hamitonian systems of arbitrary order are now worked out in detail and made more precise for the above system. In particular, a single second-order ordinary differential equation is analyzed.

Key words: Hamiltonian system of ordinary differential equations, eigenvalue problem, eigenvalues, eigenfunctions.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:6, 942–945

Bibliographic databases:

UDC: 519.624.2
Received: 19.10.2007

Citation: A. A. Abramov, V. I. Ul'yanova, L. F. Yukhno, “Nonlinear eigenvalue problem for second-order Hamiltonian systems”, Zh. Vychisl. Mat. Mat. Fiz., 48:6 (2008), 999–1002; Comput. Math. Math. Phys., 48:6 (2008), 942–945

Citation in format AMSBIB
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\paper Nonlinear eigenvalue problem for second-order Hamiltonian systems
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\issue 6
\pages 999--1002
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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 self-adjoint nonlinear eigenvalue problem for Hamiltonian systems of ordinary differential equations with singularities”, Comput. Math. Math. Phys., 48:7 (2008), 1133–1139  mathnet  crossref  isi
    2. Abramov A.A., Ul'yanova V.I., Yukhno L.F., “Multiparameter spectral problem for some weakly coupled systems of Hamiltonian equations”, Differ. Equ., 44:7 (2008), 945–951  crossref  mathscinet  zmath  isi  scopus
    3. A. A. Abramov, V. I. Ul'yanova, L. F. Yukhno, “On the index of the boundary value problem for a homogeneous Hamiltonian system of differential equations”, Comput. Math. Math. Phys., 49:3 (2009), 474–481  mathnet  crossref  mathscinet  isi
    4. E. D. Kalinin, “Solving the multiparameter eigenvalue problem for weakly coupled systems of second order Hamilton equations”, Comput. Math. Math. Phys., 55:1 (2015), 43–52  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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