Geodesic
On a Class of Operator Equations
Matematičeskie zametki, Tome 70 (2001) no. 4, pp. 544-552

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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. 
@article{MZM_2001_70_4_a5,
     author = {B. D. Gel'man},
     title = {On a {Class} of {Operator} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {544--552},
     publisher = {mathdoc},
     volume = {70},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a5/}
}
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B. D. Gel'man. On a Class of Operator Equations. Matematičeskie zametki, Tome 70 (2001) no. 4, pp. 544-552. http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a5/