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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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm766https://doi.org/10.4213/mzm766 https://www.mathnet.ru/eng/mzm/v70/i4/p544
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Abstract page: | 312 | Full-text PDF : | 193 | References: | 70 | First page: | 1 |
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