A multiplicity result for the periodically forced \(N\)-pendulum with nonzero-mean valued forcings (Q5932181)

Using different variational techniques, the author proves the existence of multiple periodic solutions for the equation of forced planar \(N\)-pendulum. The important situation when all the focing terms have nonzero-mean values is considered; although in this case the useful symmetry of the variational problem is lost, the author obtains a \(2^N\)-multiplicity result, imposing suitable restrictions on the period and amplitude of forcing terms. A demonstration is given for the particular case \(N=2\).