On solvability conditions of a boundary value problem for a nonlinear abstract functional-differential equation

A nonlinear abstract functional-differential equation in metric space is under discussion. To equations as such there can be brought, under a proper choice of a metric space, ѕclassicalї functional-differential equations not necessarily explicit, singular equations, impulsive equations, and others. The solvability conditions for boundary value problems are derived. The methods of covering mappings theory are used.