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<p>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.</p>

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Multiple Periodic Solutions of Nonlinear Oscillators with Velocity Dependent Stiffness

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月13日

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  • Alessandro Fonda,
  • Rodica Toader

摘要

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.