Comparing Various Methods of Resolving Differential Inclusions

We compare all existing methods of resolving the homogeneous differential inclusion problem. We emphasize that there is an elementary approach to construct solutions as limit of strongly convergent sequences of approximate solutions. We discuss which role plays an universal functional which measures maximal oscillations produced by admissible for the problem functions at a given one. We suggest a constructive way to generate stable solutions of the inclusions. Finally we prove higher regularity of solutions of the inclusions.