Perturbation formulas for a nonlinear eigenvalue problem for ordinary differential equations

A. A. Abramov^a, L. F. Yukhno<sup>b

a</sup> Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Moscow, Russia
^b Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

Abstract: The eigenvalue problem for a linear system of ordinary differential equations is considered. The problem is nonlinear with respect to the spectral parameter and involves generally nonlocal additional conditions specified by a Stieltjes integral. Additionally, the input data of the problem depend on a numerical parameter. Formulas giving the principal part of the variation in the solution of the eigenvalue problem under a small variation in this parameter are proposed.

Key words: system of ordinary differential equations, nonlinear eigenvalue problem, nonlocal additional conditions, perturbation theory.

UDC: 519.624

Received: 27.09.2017
Revised: 31.10.2017

DOI: 10.7868/S0044466918060042

 English version: Computational Mathematics and Mathematical Physics, 2018, 58:6, 858–862

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