Solvability conditions for nonlinear equations on a cone in a neighborhood of an anormal point

Summary: "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 a first order regularity condition."