Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 496, Pages 68–72
DOI: https://doi.org/10.31857/S268695432101001X (Mi danma157) 		 
This article is cited in 1 scientific paper (total in 1 paper)

CONTROL PROCESSES

On global solvability of nonlinear equations with parameters

A. V. Arutyunovab, S. E. Zhukovskiya

a V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russian Federation
b Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russian Federation
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DOI: https://doi.org/10.31857/S268695432101001X
Abstract: We consider smooth mappings acting from one Banach space to another and depending on a parameter belonging to a topological space. Under various regularity assumptions, sufficient conditions for the existence of global and semilocal continuous inverse and implicit functions are obtained. We consider applications of these results to the problem of continuous extension of implicit functions and to the problem of coincidence points of smooth and continuous compact mappings.
Keywords: global implicit function, implicit function extension, coincidence point.
Funding agency Grant number
Russian Science Foundation 20-11-20131
This work was supported by the Russian Science Foundation, project no. 20-11-20131.
Presented: A. B. Kurzhanski
Received: 18.08.2020
Revised: 11.12.2020
Accepted: 12.12.2020
English version:
Doklady Mathematics, 2021, Volume 103, Issue 1, Pages 57–60
DOI: https://doi.org/10.1134/S1064562421010014
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: A. V. Arutyunov, S. E. Zhukovskiy, “On global solvability of nonlinear equations with parameters”, Dokl. RAN. Math. Inf. Proc. Upr., 496 (2021), 68–72; Dokl. Math., 103:1 (2021), 57–60
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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