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

  • Antonio Garcia
  • Jaume LlibreEmail author


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.


Periodic orbit Second-order differential equation Averaging theory 

Mathematics Subject Classification (2010)

37G15 37C80 37C30 



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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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Departamento de MatemáticasUAM-IztapalapaMexico CityMexico
  2. 2.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterra, BarcelonaSpain

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