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 Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 3, Pages 490–497 (Mi zvmmf25)

On the index of the boundary value problem for a homogeneous Hamiltonian system of differential equations

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: The index of the homogeneous self-adjoint boundary value problem for the Hamiltonian systems of ordinary differential equations is introduced. It is assumed that the system has a nontrivial solution. The relationship between the index of an eigenvalue of the nonlinear eigenvalue problem and the index of the corresponding homogeneous problem is established. Properties of the index of the problem and those of the eigenvalue are examined.

Key words: Hamiltonian system of ordinary differential equations, nonlinear eigenvalue problem, eigenvalue, index of the boundary value problem.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:3, 474–481

Bibliographic databases:

UDC: 519.62

Citation: 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”, Zh. Vychisl. Mat. Mat. Fiz., 49:3 (2009), 490–497; Comput. Math. Math. Phys., 49:3 (2009), 474–481

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, “General nonlinear self-adjoint eigenvalue problem for systems of ordinary differential equations”, Comput. Math. Math. Phys., 49:4 (2009), 602–605
2. Abramov A.A., Ul'yanova V.I., Yukhno L.F., “On the general nonlinear self-adjoint spectral problem for differential-algebraic systems”, Differ. Equ., 45:7 (2009), 966–972
3. Abramov A.A., Ul'yanova V.I., Yukhno L.F., “On the number of an eigenvalue of a general nonlinear self-adjoint spectral problem for systems of ordinary differential equations”, Differ. Equ., 46:7 (2010), 1063–1067
4. 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
5. S. V. Kurochkin, “Indexing of eigenvalues of boundary value problems for Hamiltonian systems of ordinary differential equations”, Comput. Math. Math. Phys., 54:3 (2014), 439–442
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