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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
DOI:
https://doi.org/10.4213/faa3182
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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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http://mi.mathnet.ru/eng/faa3182https://doi.org/10.4213/faa3182 http://mi.mathnet.ru/eng/faa/v49/i1/p74
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This publication is cited in the following articles:
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V. N. Levchuk, “On one class of non-dissipative operators”, Zhurn. matem. fiz., anal., geom., 13:2 (2017), 173–194
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