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

Hongbin Chen·Yi Li
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Abstract

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.

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Hongbin Chen, Yi Li. 2007-03-27. Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities. https://arxiv.org/abs/math/0703818

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