Existence, Uniqueness, and Stability of Periodic Solutions of an Equation of Duffing-Type
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 stab
& Li, Y.
(2007). Existence, Uniqueness, and Stability of Periodic Solutions of an Equation of Duffing-Type. Discrete and Continuous Dynamical Systems - Series A (DCDS-A), 18 (4), 793-807.