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

Rojas, David; Torres Villarroya, Pedro José

doi:10.1016/j.nonrwa.2021.103441

1-s2.0-S146812182100153X-main.pdf (833.9Kb)

Identificadores

URI: http://hdl.handle.net/10481/71508

DOI: 10.1016/j.nonrwa.2021.103441

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Editorial

Elsevier

Materia

Periodic solution

Bouncing

Singularity

Poincaré–Birkhoff theorem

Date

2021-10-14

Referencia bibliográfica

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]

Sponsorship

Agencia Estatal de Investigación, Spain and Ministerio de Ciencia, Innovación y Universidades, Spain grants MTM2017-82348-C2-1-P and MTM2017-86795-C3-1-P

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.

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