The degree of compact multivalued perturbations of Fredholm mappings of positive index and its application to a certain optimal control problem

Earlier a topological characteristic of the degree type for multivalued perturbations of Fredholm mappings with zero index was constructed and it was assumed that the multivalued perturbation permits a single-valued approximation. In this paper, similar characteristic is constructed for multivalued perturbations of Fredholm mappings of positive index and its application is given to the problem of the existence of an optimal solution for the boundary-value problem in the theory of ordinary differential equations with feedback.