Perturbation of Fredholm eigenvalues of linear operators

We use the reduction method, which allows one to reduce the study of perturbations of multiple eigenvalues to perturbations of simple eigenvalues, to analyze the general perturbation problem for Fredholm points of the discrete spectrum of linear operator functions analytically depending on the spect...

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Bibliographic Details
Published in:Differential equations 2017-05, Vol.53 (5), p.607-616
Main Author: Rakhimov, D. G.
Format: Article
Language:English
Subjects:
Difference and Functional Equations
Differential equations
Eigenvalues
Linear equations
Linear operators
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Perturbation methods
Reduction
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Summary:We use the reduction method, which allows one to reduce the study of perturbations of multiple eigenvalues to perturbations of simple eigenvalues, to analyze the general perturbation problem for Fredholm points of the discrete spectrum of linear operator functions analytically depending on the spectral parameter. The same method is used to study a perturbation of multiple Fredholm points of the discrete Schmidt spectrum ( s -numbers) of a linear operator. We present an example of a problem on a perturbation of the domain of the Sturm–Liouville problem for a second-order differential operator.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266117050044