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Existence, uniqueness, and stability of periodic solutions of an equation of Duffing type · arXivDesk

math/0703817Mar 27, 2007Key words and phrases: Periodic solution, topological degree, stability

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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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.

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The paper addresses: Existence, uniqueness, and stability of periodic solutions of an equation of Duffing type.
We consider a second-order equation of Duffing type.

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Author comment: Key words and phrases: Periodic solution, topological degree, stability