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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2010, Volume 50, Number 1, Pages 38–43
(Mi zvmmf4810)
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This article is cited in 1 scientific paper (total in 2 paper)
On the general nonlinear selfadjoint spectral problem for systems of ordinary differential equations with singularities
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:
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.
Received: 19.05.2009
Citation:
A. A. Abramov, V. I. Ul'yanova, L. F. Yukhno, “On the general nonlinear selfadjoint spectral problem for systems of ordinary differential equations with singularities”, Zh. Vychisl. Mat. Mat. Fiz., 50:1 (2010), 38–43; Comput. Math. Math. Phys., 50:1 (2010), 32–37
Linking options:
https://www.mathnet.ru/eng/zvmmf4810 https://www.mathnet.ru/eng/zvmmf/v50/i1/p38
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