Multiple anti-periodic solutions of implicit differential inclusions on tori

Abstract We give a lower estimate of the number of anti-periodic solutions of implicit differential inclusions on tori. Our approach is based on the application of the topological essential fixed point theory, jointly with the Nielsen theory for multivalued admissible maps. Since one of the conditions is rather technical (zero topological dimension of a fixed point set), some simple illustrative examples to the main theorem are supplied. In the single-valued case of implicit differential equations, relevant arguments are still discussed in concluding remarks.