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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 2, Pages 249–254 (Mi zvmmf4824)  

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

A. A. Abramova, V. I. Ul'yanovaa, L. F. Yukhnob

a 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.

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

Bibliographic databases:

UDC: 519.624
Received: 25.06.2009

Citation: A. A. Abramov, V. I. Ul'yanova, L. F. Yukhno, “On a singular nonlinear self-adjoint spectral problem for differential-algebraic systems of equations”, Zh. Vychisl. Mat. Mat. Fiz., 50:2 (2010), 249–254; Comput. Math. Math. Phys., 50:2 (2010), 238–243

Citation in format AMSBIB
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\pages 249--254
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