This article is cited in 5 papers

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

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

a</sup> 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.

UDC: 519.62

Received: 29.09.2008

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

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