THE DEGREE OF COMPACT MULTIVALUED PERTURBATIONS OF FREDHOLM MAPPINGS OF POSITIVE INDEX AND ITS APPLICATION TO A CERTAIN OPTIMAL CONTROL PROBLEM

摘要

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