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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 315, Pages 26–33
DOI: https://doi.org/10.4213/tm4228 (Mi tm4228) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Implicit Function Theorem in a Neighborhood of an Abnormal Point

A. V. Arutyunova, K. I. Salikhovab

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
b Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
Full-text PDF (184 kB) Citations (2)
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DOI: https://doi.org/10.4213/tm4228
Abstract: We study the existence of an implicit function, defined by an equation $G(x,\sigma )=0$, in a neighborhood of an abnormal point $(x_0,\sigma _0)$. We prove that if some $\lambda $-truncation of the mapping $F(x) = G(x,\sigma _0)$ is regular in a certain direction, then the sought implicit function exists.
Funding agency Grant number
Russian Science Foundation 20-11-20131
This work is supported by the Russian Science Foundation under grant 20-11-20131.
Received: March 28, 2021
Revised: April 19, 2021
Accepted: July 12, 2021
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 315, Pages 19–26
DOI: https://doi.org/10.1134/S0081543821050035
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: A. V. Arutyunov, K. I. Salikhova, “Implicit Function Theorem in a Neighborhood of an Abnormal Point”, Optimal Control and Differential Games, Collected papers, Trudy Mat. Inst. Steklova, 315, Steklov Math. Inst., Moscow, 2021, 26–33; Proc. Steklov Inst. Math., 315 (2021), 19–26
Citation in format AMSBIB
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\by A.~V.~Arutyunov, K.~I.~Salikhova
\paper Implicit Function Theorem in a Neighborhood of an Abnormal Point
\inbook Optimal Control and Differential Games
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 315
\pages 26--33
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4228}
\crossref{https://doi.org/10.4213/tm4228}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2021
\vol 315
\pages 19--26
\crossref{https://doi.org/10.1134/S0081543821050035}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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