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

Hongbin Chen; Yi Li

doi:10.3934/dcds.2007.18.793

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2007, Volume 18, Issue 4: 793-807. Doi: 10.3934/dcds.2007.18.793

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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
2.
Department of Mathematics, The University of Iowa, Iowa City, IA 52242

Received: December 31, 2005

Revised: February 28, 2007

Published: September 2007

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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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Mathematics Subject Classification: 34C25, 34C10.

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