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Funktsional. Anal. i Prilozhen., 2004, Volume 38, Issue 4, Pages 1–5 (Mi faa121)  

This article is cited in 9 scientific papers (total in 9 papers)

An Infinite-Dimensional Version of the Borsuk–Ulam Theorem

B. D. Gel'man

Voronezh State University

Abstract: We study the solvability of the equation $a(x)=f(x)$ on a sphere in a Banach space, where $a$ is a closed surjective linear operator and $f$ is an odd $a$-compact map. We also estimate the topological dimension of the solution set and give applications of the corresponding theorem to some problems in differential equations and other fields of mathematics.

Keywords: closed surjective operator, compact map, operator equation

DOI: https://doi.org/10.4213/faa121

Full text: PDF file (134 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2004, 38:4, 239–242

Bibliographic databases:

UDC: 517.988.6
Received: 13.02.2003

Citation: B. D. Gel'man, “An Infinite-Dimensional Version of the Borsuk–Ulam Theorem”, Funktsional. Anal. i Prilozhen., 38:4 (2004), 1–5; Funct. Anal. Appl., 38:4 (2004), 239–242

Citation in format AMSBIB
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\pages 1--5
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\jour Funct. Anal. Appl.
\yr 2004
\vol 38
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\pages 239--242
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Gelman B.D., “Mnogoznachnye szhimayuschie otobrazheniya i ikh prilozheniya”, Vestn. Voronezhskogo gos. un-ta. Ser.: Fiz. Matem., 2009, no. 1, 74–86
    2. Gelman B.D., Zhuk N.M., “O beskonechnomernoi versii teoremy borsuka-ulama dlya mnogoznachnykh otobrazhenii”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2011, no. 2, 78–84  zmath  elib
    3. Zhuk N.M., “Teorema borsuka-ulama dlya mnogoznachnykh otobrazhenii v beskonechnomernykh banakhovykh prostranstvakh”, Vestnik Tambovskogo universiteta. Seriya: Estestvennye i tekhnicheskie nauki, 16:4 (2011), 1076–1078  mathscinet  elib
    4. Gelman B.D., Rydanova S.S., “Ob operatornykh uravneniyakh s syurektivnymi operatorami”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2012, no. 1, 93–93  mathscinet  zmath  elib
    5. B. D. Gel'man, “The Solution Set of a Class of Equations with Surjective Operators”, Funct. Anal. Appl., 49:1 (2015), 60–63  mathnet  crossref  crossref  zmath  isi  elib
    6. B. D. Gel'man, “How to Approach Nonstandard Boundary Value Problems”, Funct. Anal. Appl., 50:1 (2016), 31–38  mathnet  crossref  crossref  mathscinet  isi  elib
    7. B. D. Gel'man, “A version of the infinite-dimensional Borsuk-Ulam theorem for multivalued maps”, Sb. Math., 207:6 (2016), 841–853  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    8. Milojevic P.S., “Dimension of the Set of Positive Solutions To Nonlinear Equations and Applications”, Electron. J. Differ. Equ., 2016  mathscinet  isi  elib
    9. B. D. Gelman, “O teoreme Borsuka–Ulama dlya lipshitsevykh otobrazhenii v beskonechnomernom prostranstve”, Funkts. analiz i ego pril., 53:1 (2019), 79–83  mathnet  crossref  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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