Existence of Periodic Solutions for a Class of Second Order Ordinary Differential Equations

Abstract

We provide sufficient conditions for the existence of a periodic solution for a class of second order differential equations of the form \(\ddot{x}+g(x)=\varepsilon f(t, x,\dot{x},\varepsilon )\), where \(\varepsilon \) is a small parameter.

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Acknowledgements

The second author is partially supported by the Ministerio de Ciencia, Innovación y Universidades, Agencia Estatal de Investigación grants MTM2016-77278-P (FEDER), the Agència de Gestió d’Ajuts Universitaris i de Recerca grant 2017SGR1617, and the H2020 European Research Council grant MSCA-RISE-2017-777911.

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Correspondence to Jaume Llibre.

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Garcia, A., Llibre, J. Existence of Periodic Solutions for a Class of Second Order Ordinary Differential Equations. Acta Appl Math 169, 193–197 (2020). https://doi.org/10.1007/s10440-019-00295-9

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Keywords

  • Periodic orbit
  • Second-order differential equation
  • Averaging theory

Mathematics Subject Classification (2010)

  • 37G15
  • 37C80
  • 37C30