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Funktsional. Anal. i Prilozhen., 2015, Volume 49, Issue 1, Pages 74–78 (Mi faa3182)  

This article is cited in 1 scientific paper (total in 1 paper)

Brief communications

The Solution Set of a Class of Equations with Surjective Operators

B. D. Gel'man

Voronezh State University

Abstract: Operator equations of the form $A(x)=f(x)$ are studied in the case where $A$ is a closed surjective linear operator and the map $f$ is condensing with respect to $A$. Not only existence theorems are proved but also the topological dimension of the solution set of such an equation is estimated. The obtained results are applied to study the set of global solutions of a certain class of neutral-type equations.

Keywords: surjective linear operator, measure of noncompactness, condensing map, topological dimension, differential equation

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00468-а


DOI: https://doi.org/10.4213/faa3182

Full text: PDF file (140 kB)
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English version:
Functional Analysis and Its Applications, 2015, 49:1, 60–63

Bibliographic databases:

UDC: 517.988.6
Received: 17.08.2013

Citation: B. D. Gel'man, “The Solution Set of a Class of Equations with Surjective Operators”, Funktsional. Anal. i Prilozhen., 49:1 (2015), 74–78; Funct. Anal. Appl., 49:1 (2015), 60–63

Citation in format AMSBIB
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  • https://doi.org/10.4213/faa3182
  • http://mi.mathnet.ru/eng/faa/v49/i1/p74

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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. V. N. Levchuk, “On one class of non-dissipative operators”, Zhurn. matem. fiz., anal., geom., 13:2 (2017), 173–194  mathnet  crossref
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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