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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 $E_1$ and $E_2$ are Banach spaces, $a\colon E_1\to E_2$ is a continuous linear surjective operator, $f\colon E_1\to E_2$ is a nonlinear completely continuous operator. In this paper, we study existence problems for the equation $a(x)=f(x)$ and estimate the topological dimension $dim$ 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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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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