Abstract:
Consider the pendulum equation with an external periodic force and an appropriate condition on the length parameter. It is proved that there exists at least one stable periodic solution for almost every external force with zero average. The stability is understood in the Lyapunov sense.
\Bibitem{Ort13}
\by Rafael Ortega
\paper Stable Periodic Solutions in the Forced Pendulum Equation
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 6
\pages 585--599
\mathnet{http://mi.mathnet.ru/rcd150}
\crossref{https://doi.org/10.1134/S1560354713060026}
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\zmath{https://zbmath.org/?q=an:1303.34031}
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This publication is cited in the following 6 articles:
Yanxia Deng, Daniel Offin, “Stability of periodic orbits by Conley-Zehnder index theory”, Journal of Differential Equations, 314 (2022), 473
F. Wang, J. Chu, Z. Liang, “Prevalence of stable periodic solutions in the forced relativistic pendulum equation”, Discrete Contin. Dyn. Syst.-Ser. B, 23:10 (2018), 4579–4594
Z. Liang, Zh. Zhou, “Stable and unstable periodic solutions of the forced pendulum of variable length”, Taiwan. J. Math., 21:4 (2017), 791–806
J. Chu, F. Wang, “Prevalence of stable periodic solutions for duffing equations”, J. Differ. Equ., 260:11 (2016), 7800–7820
A. Boscaggin, R. Ortega, F. Zanolin, “Subharmonic solutions of the forced pendulum equation: a symplectic approach”, Arch. Math., 102:5 (2014), 459–468
R. Ortega, “A forced pendulum equation without stable periodic solutions of a fixed period”, Port Math., 71:3-4 (2014), 193–216
Citation in format AMSBIB
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