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Computational and Applied Mathematics

, Volume 37, Issue 2, pp 1550–1561 | Cite as

On the periodic solutions of the Michelson continuous and discontinuous piecewise linear differential system

  • Jaume Llibre
  • Regilene OliveiraEmail author
  • Camila Ap. B. Rodrigues
Article
  • 160 Downloads

Abstract

Applying new results from the averaging theory for continuous and discontinuous differential systems, we study the periodic solutions of two distinct versions of the Michelson differential system: a Michelson continuous piecewise linear differential system and a Michelson discontinuous piecewise linear differential system. The tools here used can be applied to general nonsmooth differential systems.

Keywords

Continuous piecewise linear differential systems Discontinuous piecewise linear differential systems Michelson system Averaging theory Periodic solutions 

Mathematics Subject Classification

34C29 34C25 37G15 

Notes

Acknowledgements

We thank to the reviewer his/her comments which help us to improve the presentation of this paper. The first author is partially supported by the MINECO grants MTM 2016-77278-P and MTM2013-40998-P, an AGAUR grant number 2014 SGR-568, the grants FP7-PEOPLE-2012-IRSES 318999 and 316338. The first two authors are also supported by the CAPES grant number 88881.030454/2013-01 from the program CSF-PVE. The second author is partially supported by the joint projects FP7-PEOPLE-2012-IRSES numbers 316338, CNPq grant “Projeto Universal 472796/2013-5” and FAPESP grant number 2014/00304-2. The third author is supported by a FAPESP grant number 2012/22000-0.

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2016

Authors and Affiliations

  • Jaume Llibre
    • 1
  • Regilene Oliveira
    • 2
    Email author
  • Camila Ap. B. Rodrigues
    • 2
  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBarcelonaSpain
  2. 2.Departamento de MatemáticaICMC-Universidade de São PauloSão CarlosBrazil

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