Multiple forced rotational solutions for the planar N-pendulum equation

This paper presents a theorem of existence of (N.N0+1)2N0 noncontractible periodic orbits of any given rotational vector with zero components for the planar forced N-pendulum equation, where N0 denotes the number of zero components of given rotational vector. We make special arrangements for masses and length instead of the nondegenerate assumption. Moreover, for rotational vectors with identical components, similar results is also obtained.