On the existence of forced oscillations of retarded functional motion equations on a class of topologically nontrivial manifolds

Using a topological approach, based on the fixed point index theory for locally compact maps on metric ANRs, we prove the existence of forced oscillations for retarded functional motion problems constrained on compact manifolds with nontrivial Euler–Poincar´e characteristic, provided that the frictional coefficient is nonzero. We do not know if an analogous result holds true in the frictionless case.