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January  2013, 33(1): 277-282. doi: 10.3934/dcds.2013.33.277

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, Spain
2. 

Departamento de Matemática, Ibilce -UNESP, 15054-000 São José do Rio Preto, Brazil

Received  February 2011 Revised  December 2011 Published  September 2012

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.
Keywords: bifurcation, stability., Duffing differential equation, averaging method, Periodic solution.
Mathematics Subject Classification: Primary: 34C23, 34C25, 34C29, 34D20, 34G1.
Citation: Jaume Llibre, Luci Any Roberto. On the periodic solutions of a class of Duffing differential equations. Discrete & Continuous Dynamical Systems, 2013, 33 (1) : 277-282. doi: 10.3934/dcds.2013.33.277
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show all references

References:
[1]

Proc. Amer. Math. Soc., 135 (2007), 3925-3932. Google Scholar

[2]

Nonlinearity, 21 (2008), 2485-2503. Google Scholar

[3]

Sammlung Viewg Heft, Viewg, Braunschweig, 41/42 (1918). Google Scholar

[4]

in: "Equadiff, Brno. Proceedings, Brno: Masaryk University,'' 9 (1997), 115-145. Google Scholar

[5]

Boo. Uni. Mat. Ital B, 3 (1989), 533-546.  Google Scholar

[6]

Universitext, Springer, 1991.  Google Scholar

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