Abstract
We provide a result on the existence of a positive periodic solution for the following class of delay equations
In particular, we find an infinite family of disjoint intervals having the following property: if the delay is within one of these intervals, then the equation admits a non-trivial and even \(2r\)-periodic solution. Furthermore, the length of these intervals is constant and depends on the size of the term \(|f'(\eta )|\), where \(\eta \) is the unique positive equilibrium point of the equation. Consequently, we can find periodic solutions for arbitrarily large delays.
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The work of M. Zamora was supported by Agencia Estatal de Investigación. Spain, project MCIU-22-PID2021-128418NA-I00.
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Gomez, A., Morales, N. & Zamora, M. Non-Trivial Periodic Solutions for a Class of Second Order Differential Equations with Large Delay. Acta Appl Math 188, 3 (2023). https://doi.org/10.1007/s10440-023-00613-2
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DOI: https://doi.org/10.1007/s10440-023-00613-2