# American Institute of Mathematical Sciences

November  2007, 18(4): 793-807. doi: 10.3934/dcds.2007.18.793

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

 1 Department of Mathematics, Xi'an Jiaotong University, Xi'an, China 2 Department of Mathematics, The University of Iowa, Iowa City, IA 52242, United States

Received  January 2006 Revised  March 2007 Published  May 2007

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.
Citation: Hongbin Chen, Yi Li. Existence, uniqueness, and stability of periodic solutions of an equation of duffing type. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 793-807. doi: 10.3934/dcds.2007.18.793
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