Abstract (EN)

We prove a set-valued Gronwall lemma and a relaxation theorem for the semilinear differential inclusion x′ ϵAx + F(t, x), x(0) = x0, where A is the infinitesimal generator of a C0-semigroup on a separable Banach space X and F: [0, T] × X ↦ X is a set-valued map. This allows us to investigate infinitesimal generators of reachable sets and variational inclusions. The results are applied to a semilinear optimal control problem with end point constraints.