Periodic motions of a class of forced infinite lattices with nearest neighbor interaction ✩

In this paper, by using a priori bounds, topological degree and limiting arguments, we study the existence of periodic solutions of a class of one-dimensional chain of particles periodically perturbed and with nearest neighbor interaction between particles. We study the necessary and sufficient conditions for the existence of periodic solutions in two cases when the number of particles is finite and infinite and obtain different results. © 2007 Elsevier Inc. All rights reserved