The stability of the equilibrium of a nonlinear planar system and application to the relativistic oscillator

DOI10.1016/j.jde.2008.11.013zbMath1175.34053OpenAlexW2098997045MaRDI QIDQ1025006

Meirong Zhang, Jifeng Chu, Jinzhi Lei

Publication date: 18 June 2009

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

Full work available at URL: https://doi.org/10.1016/j.jde.2008.11.013

zbMATH Keywords

periodic solutionsLyapunov stabilityrelativistic oscillatorBirkhoff normal formstwist coefficientplanar nonlinear systems

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Stability of solutions to ordinary differential equations (34D20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15)

Related Items (22)

Prevalence of stable periodic solutions for Duffing equations ⋮ Existence and stability of periodic solutions for a forced pendulum with time-dependent damping ⋮ Existence and stability of periodic oscillations of a smooth and discontinuous oscillator ⋮ Twist periodic solutions in the relativistic driven harmonic oscillator ⋮ Periodic solutions of pendulum-like perturbations of singular and bounded \({\varphi}\)-Laplacians ⋮ Lyapunov stability of singular planarsystems related to dispersion-managedsolitons in optical fiber ⋮ On the existence of periodic oscillations for pendulum-type equations ⋮ Lyapunov-type stability criterion for periodic generalized Camassa-Holm equations ⋮ Radial solutions of Neumann problem for periodic perturbations of the mean extrinsic curvature operator ⋮ The Lyapunov stability for the linear and nonlinear damped oscillator with time-periodic parameters ⋮ Lyapunov stability of elliptic periodic solutions of nonlinear damped equations ⋮ On Littlewood's boundedness problem for relativistic oscillators with anharmonic potentials ⋮ Relativistic pendulum and invariant curves ⋮ On Littlewood's boundedness problem for relativistic oscillators with singular potentials ⋮ Stable and unstable periodic solutions of the forced pendulum of variable length ⋮ Prevalence of stable periodic solutions in the forced relativistic pendulum equation ⋮ Optimal conditions for maximum and antimaximum principles of the periodic solution problem ⋮ The stability of the equilibrium of the damped oscillator with damping changing sign ⋮ On the periodic solutions of the relativistic driven harmonic oscillator ⋮ Stability of equilibrium solutions of autonomous and periodic Hamiltonian systems in the case of multiple resonances ⋮ A qualitative explanation of the origin of torsional instability in suspension bridges ⋮ Existence and stability of periodic oscillations of a rigid dumbbell satellite around its center of mass

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