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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 312, Pages 7–21
DOI: https://doi.org/10.4213/tm4149 (Mi tm4149) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Stable Solvability of Nonlinear Equations under Completely Continuous Perturbations

A. V. Arutyunovab, S. E. Zhukovskiya

a V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, ul. Profsoyuznaya 65, Moscow, 117997 Russia
b Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Bol'shoi Karetnyi per. 19, str. 1, Moscow, 127051 Russia
Full-text PDF (237 kB) Citations (2)
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DOI: https://doi.org/10.4213/tm4149
Abstract: For nonlinear mappings acting in Banach spaces, we examine inverse and implicit function theorems under various smoothness assumptions. For various regularity (normality) conditions imposed on such mappings, we prove that the corresponding equations have solutions under any sufficiently small (in the norm) completely continuous perturbations. A priori estimates for these solutions are obtained.
Funding agency Grant number
Russian Science Foundation 20-11-20131
Volkswagen Foundation
This work was supported by the Volkswagen Foundation. The research presented in Section 2 was performed by the second author and supported by the Russian Science Foundation under grant 20-11-20131.
Received: June 29, 2020
Revised: December 19, 2020
Accepted: December 25, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 312, Pages 1–15
DOI: https://doi.org/10.1134/S0081543821010016
Bibliographic databases:
Document Type: Article
UDC: 517.275
Language: Russian
Citation: A. V. Arutyunov, S. E. Zhukovskiy, “Stable Solvability of Nonlinear Equations under Completely Continuous Perturbations”, Function Spaces, Approximation Theory, and Related Problems of Analysis, Collected papers. In commemoration of the 115th anniversary of Academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 312, Steklov Math. Inst., Moscow, 2021, 7–21; Proc. Steklov Inst. Math., 312 (2021), 1–15
Citation in format AMSBIB
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\by A.~V.~Arutyunov, S.~E.~Zhukovskiy
\paper Stable Solvability of Nonlinear Equations under Completely Continuous Perturbations
\inbook Function Spaces, Approximation Theory, and Related Problems of Analysis
\bookinfo Collected papers. In commemoration of the 115th anniversary of Academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 312
\pages 7--21
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4149}
\crossref{https://doi.org/10.4213/tm4149}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2021
\vol 312
\pages 1--15
\crossref{https://doi.org/10.1134/S0081543821010016}
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    • This publication is cited in the following 2 articles:
    1. N. S. Borzov, T. V. Zhukovskaya, I. D. Serova, “Obyknovennye differentsialnye uravneniya i differentsialnye uravneniya s zapazdyvaniem: obschie svoistva i osobennosti”, Vestnik rossiiskikh universitetov. Matematika, 28:142 (2023), 137–154  mathnet  crossref
    2. A. V. Arutyunov, S. E. Zhukovskiy, “On implicit function theorem for locally Lipschitz equations”, Math. Program., 198 (2022), 1107–1120  crossref  mathscinet  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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