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

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

2007-03-27

arxiv.org/abs/math/0703817v1

Mathematics

Classical Analysis and ODEs

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

Scientific paper

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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