Well-posed solvability of control problems for systems of implicit differential equations

Theorems on solvability, estimates of solutions, and well-posed solvability of equations with covering mappings in the product of metric spaces are formulated. Conditions for the Nemytskii operator to be a covering operator in functional spaces are considered. Statements about covering mappings are applied to studying the controlled systems described by ordinary differential equations unsolved for the derivative. For controlled differential systems with mixed constraints on control and an additional constraint on the solution's derivative, conditions of solvability are received as well as solutions' estimates, the question of continuous dependence of solutions on parameters is investigated.