Analysis of the period map for a singular ODE related to the Liebau phenomenon

We study the positive periodic solutions of a periodically perturbed second-order nonlinear equation with a singularity, related to the so-called Liebau phenomenon, which has received great deal of interest in the past decade. Our main contribution concerns a global theorem about the monotonicity of...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2024-09, Vol.537 (2), p.128317, Article 128317
Main Authors: Burra, Lakshmi, Zanolin, Fabio
Format: Article
Language:English
Subjects:
Bifurcation
Linked twist maps
Mathematical models in cardiology
Period map
Positive solutions
Subharmonics
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Summary:We study the positive periodic solutions of a periodically perturbed second-order nonlinear equation with a singularity, related to the so-called Liebau phenomenon, which has received great deal of interest in the past decade. Our main contribution concerns a global theorem about the monotonicity of the period map for the equation with constant coefficients. Then, as applications, we prove new bifurcation results for periodic solutions (harmonic and subharmonic), as well as the presence of complex dynamics for some periodic coefficients which are meaningful from a physical point of view.
ISSN:0022-247X
DOI:10.1016/j.jmaa.2024.128317