Unboundedness in a Duffing equation with polynomial potentials

DOI10.1006/jdeq.1999.3666zbMath0947.34017OpenAlexW1982422725MaRDI QIDQ1968706

Yi Qian Wang

Publication date: 25 October 2000

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

Full work available at URL: https://doi.org/10.1006/jdeq.1999.3666

zbMATH Keywords

unbounded solutionDuffing equation

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Growth and boundedness of solutions to ordinary differential equations (34C11)

Related Items (12)

Rareness of escaping orbits of the quasi-periodic Duffing equations with polynomial potentials ⋮ A KAM theorem with large twist and finite smooth large perturbation ⋮ Boundedness for sublinear reversible systems with a nonlinear damping and periodic forcing term ⋮ Lagrange stability for impulsive Duffing equations ⋮ The coexistence of quasi-periodic and blow-up solutions in a class of Hamiltonian systems ⋮ Boundedness of solutions for Duffing equation with low regularity in time ⋮ The coexistence of quasi-periodic and blow-up solutions in a superlinear Duffing equation ⋮ Applications of the Moser's twist theorem to some impulsive differential equations ⋮ Boundedness of solutions for a class of sublinear reversible oscillators with periodic forcing ⋮ Boundedness for sublinear Duffing equations with time-dependent potentials ⋮ Longtime closeness estimates for bounded and unbounded solutions of non-recurrent Duffing equations with polynomial potentials ⋮ Quasiperiodic solutions of higher dimensional Duffing's equations via the KAM theorem.

Cites Work

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• Boundedness of solutions for Duffing-type equation
• Boundedness of solutions for polynomial potentials with \(C^2\) time dependent coefficients
• Oscillatory escape in a Duffing equation with a polynomial potential
• On the continuation of solutions of a certain non-linear differential equation
• Invariant curves and time-dependent potentials
• Boundedness for solutions of nonlinear periodic differential equations via Moser's twist theorem
• A case of boundedness in Littlewood's problem on oscillatory differential equations
• Unbounded Solutions of ÿ + g(y) = p{t)

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