Control problems for equations with a spectral parameter and a discontinuous operator under perturbations

In Banach spaces control problems for systems with a spectral parameter, an external perturbation and a discontinuous operator are considered. The theorem on resolvability for investigated problems is proved. General results are applied to control problems for distributed systems of the elliptic type with a spectral parameter and discontinuous nonlinearity under an external perturbation. Propositions on resolvability for such problems are established. Control problem with a perturbation in the Gol'dshtik mathematical model for separated flows of incompressible fluid is considered as an application.