Symmetric and periodic bouncing motions for a class of finite and infinite locally coupled superlinear systems.

We consider a class of finite-dimensional and infinite-dimensional locally coupled systems of periodic Hill-type equations with impacts. First, for finite dimensional systems, with assumptions of superlinearity on the restoring forces and boundedness on the coupling terms, we show the twist properties of the Poincaré maps on the suitably large torus in each sub-phase plane. Then, by a high-dimensional zero point theorem, it is proved the existence of infinitely many symmetric harmonic and subharmonic bouncing solutions. Second, we consider an infinite-dimensional system as a limit case of a sequence of finite-dimensional systems. By a detailed discussions for taking limits, it is proved that a sequence of even and periodic bouncing solutions of some finite-dimensional systems can converge to an even and periodic bouncing solution of the infinite-dimensional system. [ABSTRACT FROM AUTHOR]