On the periodic oscillations of \(\ddot x=g(x)\)

DOI10.1016/0022-0396(89)90076-4zbMath0701.34049OpenAlexW1994403283MaRDI QIDQ914023

Gaetano Zampieri

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0022-0396(89)90076-4

zbMATH Keywords

m-isochronismm-isochronous center

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10)

Related Items (5)

Global isochronous potentials ⋮ Completely integrable Hamiltonian systems with weak Lyapunov instability or isochrony ⋮ New periodic recurrences with applications ⋮ Period function for a class of Hamiltonian systems ⋮ Involutions of real intervals

Cites Work

• Lyapunov stability for some central forces
• Analytical theory of nonlinear oscillations. VII: The periods of the periodic solutions of the equation \(\ddot x+g(x)=0\)
• Analytical theory of non-linear oscillations. VIII: Second order conservative systems whose solutions are all oscillating with the least period \(2\pi\)
• Solving a collection of free coexistence-like problems in stability
• The potential force yielding a periodic motion whose period is an arbitrary continuous function of the amplitude of the velocity
• Nonlinear oscillations of fixed period
• Sur les périodes des solutions de l'équation différentielle x + g(x) = 0
• Non-conservative positional systems-stability
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