On Littlewood’s boundedness problem for sublinear Duffing equations

DOI10.1090/S0002-9947-00-02770-7zbMath0974.34031MaRDI QIDQ2701671

Bin Liu

Publication date: 19 February 2001

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

quasi-periodic solutionsboundedness of solutionsMoser's small twist theorem

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Growth and boundedness of solutions to ordinary differential equations (34C11) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27)

Related Items (21)

Boundedness of solutions for reversible systems ⋮ Boundedness of solutions of a quasi-periodic sublinear Duffing equation ⋮ Rareness of escaping orbits of the quasi-periodic Duffing equations with polynomial potentials ⋮ 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. ⋮ 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 ⋮ On Littlewood's boundedness problem for relativistic oscillators with singular potentials ⋮ 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 ⋮ Unbounded motions in forced Newtonian equations ⋮ Boundedness of solutions for Duffing's equations with semilinear potentials ⋮ Boundedness for sublinear Duffing equations with time-dependent potentials ⋮ Bounding solutions of a forced oscillator ⋮ Littlewood's problem for isochronous oscillators

Cites Work

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• Boundedness for solutions of nonlinear Hill's equations with periodic forcing terms via Moser's twist theorem
• Quasiperiodic motions in superquadratic time-periodic potentials
• Boundedness for solutions of superlinear Duffing equations via the twist theorem
• Aubry-Mather sets for finite-twist maps of a cylinder and semilinear Duffing equations
• Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
• Stable and Random Motions in Dynamical Systems
• Invariant curves and time-dependent potentials
• A case of boundedness in Littlewood's problem on oscillatory differential equations
• Existence of quasiperiodic solutions and Littlewood’s boundedness problem of Duffing equations with subquadratic potentials

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