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JOURNALS // Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia // Archive

Dokl. RAN. Math. Inf. Proc. Upr., 2021 Volume 496, Pages 68–72 (Mi danma157)

This article is cited 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

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.

UDC: 517

Presented: A. B. Kurzhanski
Received: 18.08.2020
Revised: 11.12.2020
Accepted: 12.12.2020

DOI: 10.31857/S268695432101001X


 English version:
Doklady Mathematics, 2021, 103:1, 57–60

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© Steklov Math. Inst. of RAS, 2024