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The pursuit of these technical objectives is organized in following tasks associated with the required intermediate goals:
Task 1 Sufficient conditions for the composition of two locally covering single-valued or set-valued mappings to be locally covering. Period: Months 1-6.
Task 2 Sufficient conditions for single-valued locally covering mapping to have a continuous inverse mapping. It will be verified whether Clarkes regularity condition implies continuity of inverse mapping in finite-dimensional linear spaces. Period: Months 1-6.
Task 3 Conditions for Lipschitz perturbed conditionally alfa covering set-valued mappings to have a covering property. Moreover, conditions for the solvability of inclusions and for the continuous dependence of the solution on a parameter will be investigated as a corollary of the theorem about Lipschitz perturbations. Period: Months 6-12.
Task 4 Properties of covering mappings in generalized metric spaces. This includes the investigation of topological properties of metric spaces, to obtain the global and local coincidence points theorems for mappings in generalized metric spaces, as well as covering properties of certain mappings of functional generalized metric spaces. Period: Months 6-12.
Task 5 Global solvability conditions for controlled differential systems defined by functional-differential equation and subject to mixed constraints. Period: Months 12-18.
Task 6 Solvability conditions for difference equations in metric spaces Difference equations. This includes conditions for the existence of equilibrium, as well as stability conditions and local stability at the equilibrium. Period: Months 12-18.
Task 7 Solvability conditions for equations in functional generalized metric spaces. The task includes the research of the solutions properties for certain functional equations formulated in the following spaces: continuous functions defined on an unbounded set, measurable functions, convex functions. Period: Months 18-24.
Task 8 First order optimality conditions for an optimal control problem of generalized type in which ordinary differential dynamics will be replaced by a Volterra equation. Period: Months 18-24.