Periodic solutions of non linear differential difference equations

In this paper we will be interested in the behaviour of long chains of coupled gravitational pendula. We will prove existence and uniqueness of periodic solutions for such chains under periodic forcing and will prove that under some smoothness assumptions the chain behaves as an uncoupled one. We will also analyse a more general class of differential difference equations and prove existence and unicity results for periodic solutions.Research partially supported by AFOSR under U.R.I, contract F49620-86-C-0131 to Northeastern University.