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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

Hongbin Chen 1, and  Yi Li 2,

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.
Keywords: stability., topological degree, Periodic solution.
Mathematics Subject Classification: 34C25, 34C1.
Citation: Hongbin Chen, Yi Li. Existence, uniqueness, and stability of periodic solutions of an equation of duffing type. Discrete & Continuous Dynamical Systems, 2007, 18 (4) : 793-807. doi: 10.3934/dcds.2007.18.793
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