Boundedness in nonlinear oscillations at resonance

DOI10.1006/jdeq.1998.3553zbMath0926.34028OpenAlexW2023391208MaRDI QIDQ1284432

Bin Liu

Publication date: 29 November 1999

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

Full work available at URL: https://doi.org/10.1006/jdeq.1998.3553

zbMATH Keywords

boundednessHamiltonian systemDuffing equationtwist theoremsemilinear

Mathematics Subject Classification ID

Related Items (45)

A note on the existence of unbounded solutions to a perturbed asymmetric oscillator ⋮ Lagrange stability for asymptotic linear Duffing equations ⋮ Quasi-periodic solutions for second order differential equation with superlinear asymmetric nonlinearities and nonlinear damping term ⋮ Aubry-Mather sets in semilinear asymmetric Duffing equations ⋮ Problems of periodic solutions for a type of Duffing equation with state-dependent delay ⋮ Invariant tori for asymptotically linear impact oscillators ⋮ Lazer-Leach type conditions on periodic solutions of Liénard equation with a deviating argument at resonance ⋮ A small twist theorem and boundedness of solutions for semilinear Duffing equations at resonance ⋮ Boundedness of solutions for a class of impact oscillators with time-dependent polynomial potentials ⋮ The existence of quasiperiodic solutions for coupled Duffing-type equations ⋮ On the existence of solutions for impulsive Duffing dynamic equations on time scales with Dirichlet boundary conditions ⋮ A Moser’s non-twist theorem for nearly integrable mappings with self-intersection property ⋮ Invariant curves of quasi-periodic reversible mappings and its application ⋮ Boundedness of semilinear Duffing equations at resonance in a critical situation ⋮ Boundedness of semilinear Duffing equations with Liouvillean frequency ⋮ Boundedness of solutions of quasi-periodic \(p\)-Laplacian equations with jumping nonlinearity ⋮ Recurrent motions in a piecewise linear oscillator ⋮ Bounded and unbounded motions in asymmetric oscillators at resonance ⋮ Invariant tori and boundedness in asymmetric oscillations. ⋮ Quasi-periodic solutions of a forced asymmetric oscillator at resonance. ⋮ Invariant tori for semilinear reversible systems. ⋮ Boundedness for the general semilinear Duffing equations via the twist theorem ⋮ On Littlewood's boundedness problem for relativistic oscillators with anharmonic potentials ⋮ The existence of invariant tori and quasiperiodic solutions of the Nosé-Hoover oscillator ⋮ Invariant tori in nonlinear oscillations ⋮ On Littlewood's boundedness problem for relativistic oscillators with singular potentials ⋮ Boundedness in forced isochronous oscillators ⋮ Boundedness of solutions for a class of second-order differential equations ⋮ Boundedness of solutions for semilinear Duffing equations ⋮ Boundedness of semilinear Duffing equations with singularity ⋮ Boundedness in nonlinear asymmetric oscillations ⋮ Invariant tori for a reversible oscillator with a nonlinear damping and periodic forcing term ⋮ Unbounded solutions of asymmetric oscillator ⋮ Quasiperiodic motions for asymmetric oscillators. ⋮ Topological Translations and Nonlinear Resonance ⋮ Boundedness of solutions for Duffing's equations with semilinear potentials ⋮ A result on the quasi-periodic solutions of forced isochronous oscillators at resonance ⋮ Harmonic solutions for a class of non-autonomous piecewise linear oscillators ⋮ Quasi-periodic solutions of forced isochronous oscillators at resonance ⋮ Boundedness and unboundedness of solutions for reversible oscillators at resonance ⋮ Lagrange stability for asymmetric Duffing equations ⋮ Boundedness in asymmetric oscillations at resonance in a critical situation ⋮ Periodic and unbounded motions in asymmetric oscillators at resonance ⋮ A new method for the boundedness of semilinear Duffing equations at resonance ⋮ Irrational rotation numbers and unboundedness of solutions of the second order differential equations with asymmetric nonlinearities

Cites Work

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