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

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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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APA

Hongbin, C., & Yi, L. (2007). Existence, uniqueness, and stability of periodic solutions of an equation of duffing type. Discrete and Continuous Dynamical Systems, 18(4), 793–807. https://doi.org/10.3934/dcds.2007.18.793

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