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- Title
Non-Trivial Periodic Solutions for a Class of Second Order Differential Equations with Large Delay.
- Authors
Gomez, Adrian; Morales, Nolbert; Zamora, Manuel
- Abstract
We provide a result on the existence of a positive periodic solution for the following class of delay equations θ ″ (t) − θ (t) + f (θ (t − r)) = 0. 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 2 r -periodic solution. Furthermore, the length of these intervals is constant and depends on the size of the term | f ′ (η) | , where η is the unique positive equilibrium point of the equation. Consequently, we can find periodic solutions for arbitrarily large delays.
- Subjects
DELAY differential equations; TOPOLOGICAL degree
- Publication
Acta Applicandae Mathematicae, 2023, Vol 188, Issue 1, p1
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-023-00613-2