Abstract We investigate the existence of classical solutions to second-order quadratic Mean-Field Games systems with local and strongly decreasing couplings form $$-\sigma m^\alpha $$ -σmα , $$\alpha \ge 2/N$$ xmlns:mml...

Suppose that X,X′ are simply-connected closed exotic 4-manifolds. It is well-known X′ obtained by an order 2 cork twist of X. We give infinite family 4-manifolds not generated any cork. This the first example admitting such a condition. prove necessary condition 4-dimensional Ozsváth-Szabó invariants for to be and as application non-contractible relatively never induced Furthermore, we estimate...