Periodic solutions for systems of forced coupled pendulum-like equations

The existence of periodic solutions for systems of forced pendulum-like equations was studied in the papers by J. A. Marlin (Internat. J. Nonlinear Mech.3 (1968), 439–447) and J. Mawhin (Internat. J. Nonlinear Mech.5 (1970), 335–339). In both works some symmetry hypotheses on the forcing terms were considered. This paper discusses the existence and multiplicity of periodic solutions of systems under consideration without any requirement on the symmetry of the forcing terms. Note that as a model example it is possible to consider the motion of N coupled pendulums (see the already mentioned paper by J. A. Marlin) or the oscillations of an N-coupled point Josephson junction with external time-dependent disturbances studied in the autonomous case by M. Levi, F. C. Hoppensteadt, and W. L. Miranker (Quart. Appl. Math.36 (1978), 167–198).