This article is cited in 1 paper

On the general nonlinear selfadjoint spectral problem for systems of ordinary differential equations with singularities

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, Moskow, 125047 Russia

Abstract: A nonlinear self-adjoint eigenvalue problem for the general linear system of ordinary differential equations is examined on an unbounded interval. A method is proposed for the approximate reduction of this problem to the corresponding problem on a finite interval. Under the assumption that the initial data are monotone functions of the spectral parameter, a method is given for determining the number of eigenvalues lying on a prescribed interval of this parameter. No direct calculation of eigenvalues is required in this method.

Key words: ordinary differential equation, nonlinear self-adjoint eigenvalue problem, eigenvalues, numerical method for determining the number of eigenvalues.

UDC: 519.62

Received: 19.05.2009

 English version: Computational Mathematics and Mathematical Physics, 2010, 50:1, 32–37

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