A topological fixed-point index theory for evolution inclusions

In the paper we construct a topological fixed-point theory for a class of s et-valued maps which appears in natural way in boundary value problems for differential inclusions. Our construction is based upon the notion of (U, V )-approximation in the sense of Ben-El-Mechaiekh and Deguire. As applicatio ns we consider initial-value problems for nonlinear evolution inclusions of the type [GRAPHICS] where the operator Lambda satisfies various monotonicity assumptions and F is an upper semi-continuous set-valued perturbation.