Geodesic
A Generalized Implicit Function Theorem
Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 3, pp. 28-35 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove a theorem generalizing the classical implicit function theorem to the case in which the derivative of the map is a surjective continuous linear operator. We do not assume that the kernel of the derivative is a complemented subspace. 
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B. D. Gel'man. A Generalized Implicit Function Theorem. Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 3, pp. 28-35. http://geodesic.mathdoc.fr/item/FAA_2001_35_3_a2/

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

[2] Trenogin V. A., Funktsionalnyi analiz, Nauka, M., 1980 | MR | Zbl

[3] Ioffe A. D., Tikhomirov V. M., Teoriya ekstremalnykh zadach, Nauka, M., 1974 | MR | Zbl

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

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

[6] Li E. B., Markus L., Osnovy teorii optimalnogo upravleniya, Nauka, M., 1972 | MR