Nonlinear spectral problem for a self-adjoint vector differential equation
- Authors: Abramov A.A.1,2, Yukhno L.F.1,2
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Affiliations:
- Dorodnitsyn Computing Center of the Russian Academy of Sciences
- Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences
- Issue: Vol 53, No 7 (2017)
- Pages: 900-907
- Section: Numerical Methods
- URL: https://journal-vniispk.ru/0012-2661/article/view/154474
- DOI: https://doi.org/10.1134/S0012266117070060
- ID: 154474
Cite item
Abstract
We consider a spectral problem that is nonlinear in the spectral parameter for a self-adjoint vector differential equation of order 2n. The boundary conditions depend on the spectral parameter and are self-adjoint as well. Under some conditions of monotonicity of the input data with respect to the spectral parameter, we present a method for counting the eigenvalues of the problem in a given interval. If the boundary conditions are independent of the spectral parameter, then we define the notion of number of an eigenvalue and give a method for computing this number as well as the set of numbers of all eigenvalues in a given interval. For an equation considered on an unbounded interval, under some additional assumptions, we present a method for approximating the original singular problem by a problem on a finite interval.
About the authors
A. A. Abramov
Dorodnitsyn Computing Center of the Russian Academy of Sciences; Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences
Author for correspondence.
Email: alalabr@ccas.ru
Russian Federation, Moscow, 119333; Moscow, 125047
L. F. Yukhno
Dorodnitsyn Computing Center of the Russian Academy of Sciences; Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences
Email: alalabr@ccas.ru
Russian Federation, Moscow, 119333; Moscow, 125047
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