Svoistva ustoicivosti dlya kvasidifferenziruemyich sistem

Stability properties of solution maps for parametric systems with finitely many inequalities and with operator equations are considered. The study of such properties is performed in a nonsmooth setting in Banach spaces, upon quasidifferentiability assumptions in the sense of Demyanov-Rubinov, through a unifying variational approach which relies on a Hoffman error bound inequality. Several solvability results in the presence of parameters are established in form of implicit multifunction theorems. Applications to the formulation of sufficient conditions for metric regularity and local openness of nondifferentiable maps are discussed, along with their employment in deriving optimality conditions for quasidifferentiable extremum problems.