On a singular nonlinear self-adjoint spectral problem for differential-algebraic systems of equations

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: The general nonlinear self-adjoint eigenvalue problem for a differential algebraic system of equations on a half-line is examined. The boundary conditions are chosen so that the solution to this system is bounded at infinity. Under certain assumptions, the original problem can be reduced to a self-adjoint system of differential equations. After certain transformations, this system, combined with the boundary conditions, forms a nonlinear self-adjoint eigenvalue problem. Requirements for the appropriate boundary conditions are clarified. Under the additional assumption that the initial data are monotone functions of the spectral parameter, a method is proposed for calculating the number of eigenvalues of the original problem that lie on a prescribed interval of this parameter.

Key words: singular differential algebraic system of equations, nonlinear self-adjoint eigenvalue problem, eigenvalue, numerical method for solving the eigenvalue problem.

UDC: 519.624

Received: 25.06.2009

 English version: Computational Mathematics and Mathematical Physics, 2010, 50:2, 238–243

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