  In this article, we prove the existence of weak solutions as well as the
existence and uniqueness of strong solutions for McKean-Vlasov multivalued
stochastic differential equations with oblique subgradients (MVMSDEswOS, for
short) by means of the equations of Euler type and Skorohod's representation
theorem. For this type of equation, compared with the method in [19,13], since
we can't use the maximal monotony property of its constituent subdifferential
operator, some different specific techniques are applied to solve our problems.
Afterwards, we give an example for MVMSDEswOS with time-dependent convex
constraints, which can be reduced to MVMSDEswOS. Finally, we consider an
optimal control problem and establish the dynamic programming principle for the
value function.
