Abstract
We are concerned with the existence, multiplicity and distribution of the even and periodic solutions of a class of symmetric superlinear Hill's equations with impact. We transform the impact phase-plane into a whole phase-plane by a coordinate transformation and, we prove the existence of infinite numbers of symmetric harmonic and subharmonic solutions of forced impactors as well as the densely distribution of symmetric subharmonic solutions of the unforced equations under some superlinear assumption about time-mapping. We also develop a lemma on sufficient condition for symmetric periodic solutions to symmetric second order equations.
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