Large deviations of multiscale multivalued McKean-Vlasov stochastic systems

This work concerns about multiscale multivalued McKean-Vlasov stochastic systems. First of all, we use a contractive mapping principle to establish the well-posedness for fully coupled multivalued McKean-Vlasov stochastic systems under non-Lipschitz conditions. Then for multiscale multivalued McKean-Vlasov stochastic systems with small noises, we prove a large deviation principle by a weak convergence approach. As a by-product, two averaging principles are obtained.