Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities

Details Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities

2007-03-27

arxiv.org/abs/math/0703818v1

Mathematics

Classical Analysis and ODEs

Keywords: Duffing equation; Periodic solution; Stability

Scientific paper

We study the stability and exact multiplicity of periodic solutions of the Duffing equation with cubic nonlinearities. We obtain sharp bounds for h such that the equation has exactly three ordered T-periodic solutions. Moreover, when h is within these bounds, one of the three solutions is negative, while the other two are positive. The middle solution is asymptotically stable, and the remaining two are unstable.

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