On the periodic solutions of a class of Duffing differentialequations

Jaume Llibre; Luci Any Roberto

doi:10.3934/dcds.2013.33.277

Article Contents

2013, Volume 33, Issue 1: 277-282. Doi: 10.3934/dcds.2013.33.277

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On the periodic solutions of a class of Duffing differential equations

Jaume Llibre^1, and
Luci Any Roberto^2,

1.
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia
2.
Departamento de Matemática, Ibilce -UNESP, 15054-000 São José do Rio Preto

Received: January 31, 2011

Revised: November 30, 2011

Published: December 2012

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Abstract

In this work we study the periodic solutions, their stability and bifurcation for the class of Duffing differential equation $x''+ \epsilon C x'+ \epsilon^2 A(t) x +b(t) x^3 = \epsilon^3 \Lambda h(t)$, where $C>0$, $\epsilon>0$ and $\Lambda$ are real parameter, $A(t)$, $b(t)$ and $h(t)$ are continuous $T$--periodic functions and $\epsilon$ is sufficiently small. Our results are proved using the averaging method of first order.

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Mathematics Subject Classification: Primary: 34C23, 34C25, 34C29, 34D20, 34G15.

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References

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