Geodesic
Covering of nonlinear maps on a cone in neighborhoods of irregular points
Matematičeskie zametki, Tome 77 (2005) no. 4, pp. 483-497.

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Inverse function theorems for smooth nonlinear maps defined on convex cones in Banach spaces in a neighborhood of an irregular point are considered. The corresponding covering theorem is proved. The proofs are based on a Banach open mapping theorem for convex cones in Banach spaces, which is also proved in the paper. Sufficient conditions for tangency to the zero set of a nonlinear map without a priori regularity assumptions are obtained. 
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A. V. Arutyunov. Covering of nonlinear maps on a cone in neighborhoods of irregular points. Matematičeskie zametki, Tome 77 (2005) no. 4, pp. 483-497. http://geodesic.mathdoc.fr/item/MZM_2005_77_4_a0/

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