Boundedness for the general semilinear Duffing equations via the twist theorem

DOI10.1016/j.jde.2011.09.019zbMath1241.34041OpenAlexW2019532750MaRDI QIDQ649748

Lei Jiao, Yi Qian Wang, Da-Xiong Piao

Publication date: 6 December 2011

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2011.09.019

zbMATH Keywords

canonical transformationHamiltonian systemboundedness of solutionsMoser's small twist theoremmethod of principle integral

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Growth and boundedness of solutions to ordinary differential equations (34C11) Dynamical aspects of twist maps (37E40)

Related Items (14)

Lagrange stability for asymptotic linear Duffing equations ⋮ Quasi-periodic solutions for the general semilinear Duffing equations with asymmetric nonlinearity and oscillating potential ⋮ A KAM theorem for quasi-periodic non-twist mappings and its application ⋮ Boundedness of solutions for a class of impact oscillators with time-dependent polynomial potentials ⋮ A KAM theorem with large twist and finite smooth large perturbation ⋮ Boundedness of semilinear Duffing equations with Liouvillean frequency ⋮ Boundedness of solutions of quasi-periodic \(p\)-Laplacian equations with jumping nonlinearity ⋮ Unnamed Item ⋮ Boundedness of solutions for semilinear Duffing equations ⋮ Boundedness of semilinear Duffing equations with singularity ⋮ Applications of the Moser's twist theorem to some impulsive differential equations ⋮ Longtime closeness estimates for bounded and unbounded solutions of non-recurrent Duffing equations with polynomial potentials ⋮ Boundedness in asymmetric oscillations at resonance in a critical situation ⋮ A new method for the boundedness of semilinear Duffing equations at resonance

Cites Work

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