Forced oscillations on manifolds and multiplicity results for periodically perturbed autonomous systems

DOI10.1016/S0377-0427(99)00259-9zbMath0936.37038OpenAlexW2058119957MaRDI QIDQ1963893

Maria Patrizia Pera, Marco Spadini, Massimo Furi

Publication date: 24 May 2000

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(99)00259-9

zbMATH Keywords

multiplicityperiodic solutionsvariational methodsdifferentiable manifoldsimplicit function methodsperiodically perturbed autonomous systems

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Forced motions for nonlinear problems in mechanics (70K40) Dynamical systems in classical and celestial mechanics (37N05)

Related Items (6)

Branches of forced oscillations induced by a delayed periodic force ⋮ Multiplicity of forced oscillations for the spherical pendulum acted on by a retarded periodic force ⋮ Branches of forced oscillations for a class of constrained ODEs: a topological approach ⋮ A note on topological methods for a class of differential-algebraic equations ⋮ About the notion of non-T -resonance and applications to topological multiplicity results for ODEs on differentiable manifolds ⋮ Periodic perturbations of constrained motion problems on a class of implicitly defined manifolds

Cites Work

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• A continuation principle for periodic solutions of forced motion equations on manifolds and applications to bifurcation theory
• Multiplicity of forced oscillations for the spherical pendulum
• Branches of forced oscillations for periodically perturbed second-order autonomous ODEs on manifolds
• On the genericity of the multiplicity results for forced oscillations on compact manifolds
• On the set of harmonic solutions of periodically perturbed autonomous differential equations on manifolds

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