Geodesic
Solvability conditions for nonlinear equations on a cone in a neighborhood of an anormal point
Trudy Instituta matematiki i mehaniki, Dynamical systems and control problems, Tome 11 (2005) no. 1, pp. 26-31 
A. V. Arutyunov. Solvability conditions for nonlinear equations on a cone in a neighborhood of an anormal point. Trudy Instituta matematiki i mehaniki, Dynamical systems and control problems, Tome 11 (2005) no. 1, pp. 26-31. http://geodesic.mathdoc.fr/item/TIMM_2005_11_1_a2/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

An operator equation described by a smooth nonlinear mapping acting in Banach spaces is considered. A solution of this equation that belongs to a given convex closed cone is sought. A condition of 2-regularity under which the equation in a neighborhood of a given point has a solution satisfying a linear-root estimate is presented. The introduced condition of 2-regularity is substantially weaker than the known Robinson condition, which is the first order regularity condition.

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