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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 4, Pages 599–609 (Mi zvmmf10187)  

This article is cited in 2 scientific papers (total in 2 papers)

A nonlinear singular eigenvalue problem for a Hamiltonian system of differential equations with redundant condition

A. A. Abramovab, L. F. Yukhnocd

a Dorodnicyn Computing Center, Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
b Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia (MFTI)
c Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia
d National Research Nuclear University (Moscow Engineering Physics Institute, MEPHI), Kashirskoe sh. 31, Moscow, 115409, Russia

Abstract: A nonlinear eigenvalue problem for a self-adjoint Hamiltonian system of differential equations is examined on an infinite half-line. It is assumed that the original data (that is, the system matrix and the matrix of boundary conditions) satisfy certain monotonicity conditions for the spectral parameter. In addition to the initial condition and the requirement that the solution be bounded on infinity, a redundant nonlocal condition specified by a Stieltjes integral is imposed. In order to make the resulting problem nontrivially solvable, it is replaced by an auxiliary problem, which is consistent subject to all the above conditions. This auxiliary problem is examined, and a numerical method that solves it is given.

Key words: singular Hamiltonian system of differential equations, nonlinear self-adjoint eigenvalue problem, eigenvalues, nonlocal conditions, redundant conditions, numerical method for counting eigenvalues.

DOI: https://doi.org/10.7868/S004446691504002X

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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:4, 597–606

Bibliographic databases:

UDC: 519.624
MSC: Primary 34L16; Secondary 34B40, 34L30
Received: 29.10.2014

Citation: A. A. Abramov, L. F. Yukhno, “A nonlinear singular eigenvalue problem for a Hamiltonian system of differential equations with redundant condition”, Zh. Vychisl. Mat. Mat. Fiz., 55:4 (2015), 599–609; Comput. Math. Math. Phys., 55:4 (2015), 597–606

Citation in format AMSBIB
\by A.~A.~Abramov, L.~F.~Yukhno
\paper A nonlinear singular eigenvalue problem for a Hamiltonian system of~differential equations with redundant condition
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2015
\vol 55
\issue 4
\pages 599--609
\jour Comput. Math. Math. Phys.
\yr 2015
\vol 55
\issue 4
\pages 597--606

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    This publication is cited in the following articles:
    1. A. A. Abramov, L. F. Yukhno, “Solving some problems for systems of linear ordinary differential equations with redundant conditions”, Comput. Math. Math. Phys., 57:8 (2017), 1277–1284  mathnet  crossref  crossref  isi  elib
    2. L. D. Akulenko, A. A. Gavrikov, S. V. Nesterov, “Numerical solution of vector Sturm–Liouville problems with Dirichlet conditions and nonlinear dependence on the spectral parameter”, Comput. Math. Math. Phys., 57:9 (2017), 1484–1497  mathnet  crossref  crossref  isi  elib  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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