Lyapunov stability for regular equations and applications to the Liebau phenomenon

DOI10.3934/DCDS.2018204zbMath1477.34067OpenAlexW2809421136MaRDI QIDQ1661191

José Ángel Cid, Feng Wang, Mirosława Zima

Publication date: 16 August 2018

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2018204

zbMATH Keywords

Lyapunov stabilityKAM theoryMoser twist theoremregular equationLiebau phenomenon

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Stability of solutions to ordinary differential equations (34D20) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Positive solutions to nonlinear boundary value problems for ordinary differential equations (34B18) Applications of boundary value problems involving ordinary differential equations (34B60)

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Existence and stability of periodic oscillations of a smooth and discontinuous oscillator ⋮ Dynamics of a fluid equation with Neumann boundary conditions ⋮ Lyapunov stability of singular planarsystems related to dispersion-managedsolitons in optical fiber ⋮ An abstract averaging method with applications to differential equations ⋮ A relationship between linear stability and index of oscillations for Lagrangian equation at higher order zones ⋮ Radial stability of periodic orbits of damped Keplerian-like systems ⋮ Nonnegative oscillations for a class of differential equations without uniqueness: a variational approach ⋮ Existence results for damped regular equations under periodic or Neumann boundary conditions ⋮ Lyapunov stability of periodic solutions of Brillouin type equations

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