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Existence, uniqueness, and stability of periodic solutions of an equation of Duffing type

Hongbin Chen·Yi Li
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Abstract

We consider a second-order equation of Duffing type. Bounds for the derivative of the restoring force are given which ensure the existence and uniqueness of a periodic solution. Furthermore, the unique periodic solution is asymptotically stable with sharp rate of exponential decay. In particular, for a restoring term independent of the variable $t$, a necessary and sufficient condition is obtained which guarantees the existence and uniqueness of a periodic solution that is stable.

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Hongbin Chen, Yi Li. 2007-03-27. Existence, uniqueness, and stability of periodic solutions of an equation of Duffing type. https://arxiv.org/abs/math/0703817

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