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

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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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     author = {A. V. Arutyunov},
     title = {Solvability conditions for nonlinear equations on a~cone in a~neighborhood of an anormal point},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {26--31},
     publisher = {mathdoc},
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     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2005_11_1_a2/}
}
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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/