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Harmonic and subharmonic solutions for superlinear damped Duffing equation. (English) Zbl 1281.34058

The authors claim to prove the existence of harmonic and subharmonic solutions for a damped Duffing equation of the form \[ x''(t) + Cx'(t) + g(x(t)) = 0, \] with \(C\geq0\) and a superlinear condition on the nonlinearity, by making use of a generalized version of the Poincaré-Birkhoff theorem due to W. Y. Ding. In my opinion, the main result should be considered under suspicion, because any version of the Poincaré-Birkhoff theorem requires the area-preserving character of the Poincaré map, a condition which is violated if \(C>0\).

MSC:

34C25 Periodic solutions to ordinary differential equations
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