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We prove the existence and multiplicity of periodic solutions of bouncingtype for a second-order differential equation with a weak repulsivesingularity. Such solutions can be catalogued according to the minimal periodand the number of elastic collisions with the singularity in each period. Theproof relies on the Poincar\'e-Birkhoff Theorem.

Periodic bouncing solutions of the Lazer-Solimini equation with weak repulsive singularity