Existence, uniqueness, and stability of periodic solutions of an equation of Duffing type
Hongbin Chen, Yi Li
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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