This article is cited in 5 papers

On the self-adjoint nonlinear eigenvalue problem for Hamiltonian systems of ordinary differential equations with singularities

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: Certain properties of the nonlinear self-adjoint eigenvalue problem for Hamiltonian systems of ordinary differential equations with singularities are examined. Under certain assumptions on the way in which the matrix of the system and the matrix specifying the boundary condition at a regular point depend on the spectral parameter, a numerical method is proposed for determining the number of eigenvalues lying on a prescribed interval of the spectral parameter.

Key words: Hamiltonian system of ordinary differential equations, nonlinear eigenvalue problem, eigenvalue, numerical method for determining the number of eigenvalues.

UDC: 519.624.1

Received: 19.10.2007

 English version: Computational Mathematics and Mathematical Physics, 2008, 48:7, 1133–1139

Bibliographic databases:

• 
•