Periodic bouncing solutions of the Lazer–Solimini equation with weak repulsive singularity. (April 2022)

• Record Type: Journal Article
• Authors: Rojas, David; Torres, Pedro J.
• Is Part Of: Nonlinear analysis. Volume 64(2022)
• Publication Date: 2022-04
• Subjects: Periodic solution -- Bouncing -- Singularity -- Poincaré–Birkhoff theorem; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103441
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: 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.