On Analytic Perturbations of Linear Equations in the Case of Incomplete Generalized Jordan Set

Based on the methods of the theory of bifurcations, the problem of perturbation of linear equations by small analytic terms is considered. In contrast to the work by Trenogin [9], the case of an incomplete generalized Jordan set of a linear Fredholm operator acting from one Banach space to another B...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2024, Vol.278 (4), p.633-646
Main Authors: Rakhimov, D. G., Akhmadzhanova, D.
Format: Article
Language:English
Subjects:
Banach spaces
Bifurcation theory
Linear equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Perturbation
Regularization
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Summary:Based on the methods of the theory of bifurcations, the problem of perturbation of linear equations by small analytic terms is considered. In contrast to the work by Trenogin [9], the case of an incomplete generalized Jordan set of a linear Fredholm operator acting from one Banach space to another Banach space is studied. A technique is proposed that uses the regularization of the Fredholm operator by a specially constructed finite-dimensional operator.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-06945-0