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

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

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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• http://mi.mathnet.ru/eng/zvmmf/v48/i6/p999

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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 self-adjoint nonlinear eigenvalue problem for Hamiltonian systems of ordinary differential equations with singularities”, Comput. Math. Math. Phys., 48:7 (2008), 1133–1139
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
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
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
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