Randomized trial demonstrates the existence of periodic solutions in nonlinear oscillators, highlighting advanced mathematical frameworks.
By the use of the Poincaré–Birkhoff theorem, we generalize several results on the existence and multiplicity of periodic solutions for scalar second order differential equations with a periodic nonlinearity, the paradigm of which is the pendulum equation. As a particular case, we extend a recent result by Amster, Cid, and Mawhin on a relativistic model of the pendulum.
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Fonda et al. (2026) studied this question.
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