Periodic bouncing solutions of the Lazer–Solimini equation with weak repulsive singularity Rojas, David Torres Villarroya, Pedro José Periodic solution Bouncing Singularity Poincaré–Birkhoff theorem We are grateful to Rafael Ortega for bringing to our attention the position-energy system that has been crucial for the regularization of collisions. We also thank the anonymous referees for their valuable comments and suggestions that contributed to improve the initial version of the paper. This work has been realized thanks to the Agencia Estatal de Investigaci´on, Spain and Ministerio de Ciencia, Innovaci´on y Universidades, Spain grants MTM2017-82348-C2-1-P and MTM2017-86795-C3-1-P. We prove the existence and multiplicity of periodic solutions of bouncing type for a second-order differential equation with a weak repulsive singularity. Such solutions can be cataloged according to the minimal period and the number of elastic collisions with the singularity in each period. The proof relies on the Poincaré–Birkhoff Theorem. 2021-11-15T08:50:35Z 2021-11-15T08:50:35Z 2021-10-14 journal article David Rojas, Pedro J. Torres, Periodic bouncing solutions of the Lazer–Solimini equation with weak repulsive singularity, Nonlinear Analysis: Real World Applications, Volume 64, 2022, 103441, ISSN 1468-1218, [https://doi.org/10.1016/j.nonrwa.2021.103441] http://hdl.handle.net/10481/71508 10.1016/j.nonrwa.2021.103441 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ open access Atribución-NoComercial-SinDerivadas 3.0 España Elsevier