Boundedness of solutions for polynomial potentials with \(C^2\) time dependent coefficients

DOI10.1007/BF00920044zbMath0957.34034OpenAlexW2128182015MaRDI QIDQ1366333

Jiangong You, Yi Qian Wang

Publication date: 26 March 2001

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00920044

zbMATH Keywords

solutionsboundednessquasiperiodic solutionperiodic functions

Mathematics Subject Classification ID

Growth and boundedness of solutions to ordinary differential equations (34C11) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27)

Related Items (16)

Boundedness of solutions for non-linear quasi-periodic differential equations with Liouvillean frequency ⋮ Oscillatory escape in a Duffing equation with a polynomial potential ⋮ The existence of quasiperiodic solutions for coupled Duffing-type equations ⋮ Rareness of escaping orbits of the quasi-periodic Duffing equations with polynomial potentials ⋮ Boundedness for sublinear reversible systems with a nonlinear damping and periodic forcing term ⋮ On Littlewood's boundedness problem for relativistic oscillators with anharmonic potentials ⋮ Boundedness of solutions in a class of Duffing equations with oscillating potentials ⋮ Unboundedness in a Duffing equation with polynomial potentials ⋮ The coexistence of quasi-periodic and blow-up solutions in a class of Hamiltonian systems ⋮ On Littlewood's boundedness problem for relativistic oscillators with singular potentials ⋮ Existence of quasi-periodic solutions and Littlewood's boundedness problem of sub-linear impact oscillators ⋮ Boundedness of solutions for a class of sublinear reversible oscillators with periodic forcing ⋮ 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 ⋮ Longtime closeness estimates for bounded and unbounded solutions of non-recurrent Duffing equations with polynomial potentials

Cites Work

• 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
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