Existence of quasiperiodic solutions and Littlewood’s boundedness problem of Duffing equations with subquadratic potentials

DOI10.1016/S0362-546X(97)00709-8zbMath0927.34021OpenAlexW2026544014WikidataQ127872656 ScholiaQ127872656MaRDI QIDQ4238382

Jiangong You, Tassilo Kuepper

Publication date: 18 May 1999

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(97)00709-8

zbMATH Keywords

Duffing equationquasiperiodic solutionsubquadratic potentialMoser twist theoremLagrangian stabilityLittlewood boundedness problem

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27)

Related Items (29)

Boundedness of solutions for reversible systems ⋮ Boundedness of solutions of a quasi-periodic sublinear Duffing equation ⋮ Boundedness of solutions for nonlinear reversible system at resonance ⋮ Invariant curves of quasi-periodic reversible mappings and its application ⋮ Subharmonic bouncing solutions for a class of sublinear impact oscillators with indefinite weight ⋮ Boundedness for sublinear reversible systems with a nonlinear damping and periodic forcing term ⋮ Boundedness of solutions for a class of reversible systems. ⋮ Boundedness problem for solutions of semilinear asymmetric equations. ⋮ On Littlewood’s boundedness problem for sublinear Duffing equations ⋮ Dynamics in coupled oscillators with recurrent/random forcing, a PDE approach. ⋮ Invariant tori for semilinear reversible systems. ⋮ On Littlewood's boundedness problem for relativistic oscillators with anharmonic potentials ⋮ Lagrangian stability of a class of second-order periodic systems ⋮ Lagrangian stability of a class of second-order periodic systems ⋮ Boundedness of solutions for sublinear reversible systems ⋮ On Littlewood's boundedness problem for relativistic oscillators with singular potentials ⋮ Boundedness of solutions for sublinear reversible systems ⋮ Boundedness of solutions of nonlinear \(p\)-Laplacian ⋮ Existence of quasi-periodic solutions and Littlewood's boundedness problem of sub-linear impact oscillators ⋮ Invariant tori for a reversible oscillator with a nonlinear damping and periodic forcing term ⋮ Boundedness of solutions for a class of sublinear reversible oscillators with periodic forcing ⋮ Boundedness of solutions for a class of second-order periodic systems ⋮ Boundedness of solutions for a class of second-order differential equation with singularity ⋮ Unbounded motions in forced Newtonian equations ⋮ Boundedness of solutions for Duffing's equations with semilinear potentials ⋮ Boundedness of solutions for semilinear Duffing equations ⋮ Boundedness for sublinear Duffing equations with time-dependent potentials ⋮ Escaping orbits are rare in the quasi-periodic Littlewood boundedness problem ⋮ Quasiperiodic solutions of higher dimensional Duffing's equations via the KAM theorem.

Cites Work

• Boundedness for solutions of nonlinear Hill's equations with periodic forcing terms via Moser's twist theorem
• Quasiperiodic motions in superquadratic time-periodic potentials
• Critical point theory and Hamiltonian systems
• Boundedness for solutions of superlinear Duffing equations via the twist theorem
• Boundedness in Periodically Forced Second Order Conservative Systems
• A case of boundedness in Littlewood's problem on oscillatory differential equations
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