B. D. Gel'man, “On a Class of Operator Equations”, Mat. Zametki, 70:4 (2001), 544–552; Math. Notes, 70:4 (2001), 494

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Matematicheskie Zametki, 2001, Volume 70, Issue 4, Pages 544–552
DOI: https://doi.org/10.4213/mzm766 (Mi mzm766)

This article is cited in 6 scientific papers (total in 6 papers)

On a Class of Operator Equations

B. D. Gel'man

Voronezh State University

Full-text PDF (207 kB) Citations (6)

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DOI: https://doi.org/10.4213/mzm766

Abstract: We assume that

E_{1}

$E_1$ and

E_{2}

$E_2$ are Banach spaces,

a : E_{1} \to E_{2}

$a\colon E_1\to E_2$ is a continuous linear surjective operator,

f : E_{1} \to E_{2}

$f\colon E_1\to E_2$ is a nonlinear completely continuous operator. In this paper, we study existence problems for the equation

a (x) = f (x)

$a(x)=f(x)$ and estimate the topological dimension

d i m

$dim$ of the set of solutions.

Received: 03.04.2000
Revised: 19.10.2000

English version:
Mathematical Notes, 2001, Volume 70, Issue 4, Pages 494–501
DOI: https://doi.org/10.1023/A:1012376602648

Bibliographic databases:

UDC: 517.988.6

Language: Russian

Citation: B. D. Gel'man, “On a Class of Operator Equations”, Mat. Zametki, 70:4 (2001), 544–552; Math. Notes, 70:4 (2001), 494–501

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm766

https://doi.org/10.4213/mzm766

https://www.mathnet.ru/eng/mzm/v70/i4/p544

This publication is cited in the following 6 articles:

B. D. Gel'man, “On topological properties of the set of solutions of operator inclusions with a multi-valued Lipschitz right-hand side”, Russian Math. (Iz. VUZ), 65:5 (2021), 4–7
B. D. Gel'man, “A Hybrid Fixed-Point Theorem for Set-Valued Maps”, Math. Notes, 101:6 (2017), 951–959
B. D. Gel'man, “How to Approach Nonstandard Boundary Value Problems”, Funct. Anal. Appl., 50:1 (2016), 31–38
Milojevic P.S., “Dimension of the Set of Positive Solutions To Nonlinear Equations and Applications”, Electron. J. Differ. Equ., 2016
Gelman B.D., Rydanova S.S., “Ob operatornykh uravneniyakh s syurektivnymi operatorami”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2012, no. 1, 93–93 On operator equations with surjective operators
Gelman B.D., Kalabukhova S.N., “Ob uplotnyayuschikh vozmuscheniyakh lineinykh syur'ektivnykh operatorov”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2011, no. 1, 120–127 On condensing perturbations of linear surjective operators

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Full-text PDF :	212
References:	86
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