Multivalent guiding function in a problem on existence of periodic solutions of some classes of differential inclusions

We propose to use the multivalent guiding function for the study of periodic solutions of some classes of differential inclusions. More precisely, we consider the periodic problem for nonlinear systems described by differential inclusions with both convex right-hand side and with nonconvex right-hand side. The latter include differential inclusions with a regular right-hand side. Note that the class of regular multimaps is wide enough. It includes, for example, bounded almost lower semicontinuous multimaps with compact values.