Geodesic
The Solution Set of a Class of Equations with Surjective Operators
Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 1, pp. 74-78 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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B. D. Gel'man. The Solution Set of a Class of Equations with Surjective Operators. Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 1, pp. 74-78. http://geodesic.mathdoc.fr/item/FAA_2015_49_1_a6/

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