This article is cited in 4 papers

Nonlinear eigenvalue problem for second-order Hamiltonian systems

A. A. Abramov^a, V. I. Ul'yanova^a, L. F. Yukhno<sup>b

a</sup> 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.

UDC: 519.624.2

Received: 19.10.2007

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

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