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. 
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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/

[1] Bobylev N. A., Emelyanov S. V., Korovin S. K., Geometricheskie metody v variatsionnykh zadachakh, Magistr, M., 1998

[2] Ricceri B., “On the topological dimension of the solution set of a class of nonlinear equations”, C. R. Acad. Sci. Paris, 325 (1997), 65–70 | MR | Zbl

[3] Fitzpatrick P. M., Massabo I., Pejsachowicz I., “On the covering dimension of the set of solutions of some nonlinear equations”, Trans. Amer. Math. Soc., 296:2 (1986), 777–798 | DOI | MR | Zbl

[4] Michael E., “Continuous selections, 1”, Ann. of Math., 63:2 (1956), 361–382 | DOI | MR | Zbl

[5] Krasnoselskii M. A., Zabreiko P. P., Geometricheskie metody nelineinogo analiza, Nauka, M., 1975

[6] Borisovich Yu. G., Gelman B. D., Myshkis A. D., Obukhovskii V. V., Vvedenie v teoriyu mnogoznachnykh otobrazhenii, Voronezhskii gosuniversitet, Voronezh, 1986 | Zbl

[7] Borisovich Yu. G., Gelman B. D., Myshkis A. D., Obukhovskii V. V., “Topologicheskie metody v teorii nepodvizhnykh tochek mnogoznachnykh otobrazhenii”, UMN, 35:1 (1980), 59–126 | MR | Zbl

[8] Aleksandrov P. S., Pasynkov B. A., Vvedenie v teoriyu razmernosti, Nauka, M., 1973

[9] Gelman B. D., “Topologicheskie svoistva mnozhestva nepodvizhnykh tochek mnogoznachnykh otobrazhenii”, Matem. sb., 188:12 (1997), 33–56 | MR | Zbl