On a nonlinear spectral problem
- Authors: Kachalov V.I.1
-
Affiliations:
- NRU “MPEI”
- Issue: Vol 71, No 2 (2025): Modern Methods of Theory of Boundary Value Problems. Pontryagin Readings — XXXV
- Pages: 233-239
- Section: Articles
- URL: https://journals.rcsi.science/2413-3639/article/view/327828
- DOI: https://doi.org/10.22363/2413-3639-2025-71-2-233-239
- EDN: https://elibrary.ru/MUMPFR
- ID: 327828
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Abstract
The problem of perturbation of the spectrum of a linear operator by a linear operator is solved thanks to the introduced concepts of holomorphic families of operators of type (A) and in the sense of Kato. The Rayleigh-Schr¨odinger series constructed in this case already converged in the usual sense, and not asymptotically. In this paper, conditions for holomorphy with respect to a small parameter of eigenpairs are found in the situation when a linear operator is perturbed by a nonlinear operator generated by a product in a Banach algebra.
About the authors
V. I. Kachalov
NRU “MPEI”
Author for correspondence.
Email: vikachalov@rambler.ru
Moscow, Russia
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