Periodic solutions of a system of coupled oscillators with one-sided superlinear retraction forces

We generalize the phase-plane method approach introduced in [9] to the case of higher dimensions. To this aim, the phase-space is assumed to be decomposable as a product of planes, where the cor- responding components of the solutions can be controlled by means of suitable plane curves. We then apply our general result to the periodic problem associated to a system of coupled oscillators, with retraction forces having a linear growth, or with one-sided superlinear nonlineari- ties.