Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities

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We study the stability and exact multiplicity of periodic solutions of the Duffing equation with cubic nonlinearities. We obtain sharp bounds for h such that the equation has exactly three ordered T-periodic solutions. Moreover, when h is within these bounds, one of the three solutions is negative, while the other two are positive. The middle solution is asymptotically stable, and the remaining two are unstable.
Keywords: Duffing equation; Periodic solution; Stability

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Classical Analysis and ODEs, 34C10; 34C25

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http://salesiana.dossiersoluciones.com/handle/123456789/126527

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0703818
 http://arxiv.org/abs/math/0703818

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arXiv