Relaxation result for differential inclusions with Stieltjes derivative

Abstract

The aim of this paper is to provide a Filippov-Wa\.{z}ewski Relaxation Theorem for the very general setting of Stieltjes differential inclusions. New relaxation results can be deduced for generalized differential problems, for impulsive differential inclusions with multivalued impulsive maps and possibly countable impulsive moments and also for dynamic inclusions on time scales.