  The work concerns multivalued McKean-Vlasov stochastic differential
equations. First of all, we prove the existence and uniqueness of strong
solutions for multivalued McKean-Vlasov stochastic differential equations with
non-Lipschitz coefficients. Then, the classical It\^{o}'s formula is extended
to that for multivalued McKean-Vlasov stochastic differential equations.
Finally, the asymptotic stability of second moments and the almost surely
asymptotic stability for their solutions in terms of a Lyapunov function are
shown.
