Periodic solutions for planar autonomous systems with nonsmooth periodic perturbations

DOI10.1016/j.jmaa.2007.05.086zbMath1140.34018arXiv0709.4418OpenAlexW2091755411MaRDI QIDQ2473987

O. Yu. Makarenkov, Paolo Nistri

Publication date: 5 March 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.4418

zbMATH Keywords

periodic solutionstopological degreecharacteristic multipliersplanar autonomous systemslimit sysclesnonsmooth periodic perturbations

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Perturbations of ordinary differential equations (34D10)

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Multiple positive solutions of singular nonlinear Sturm-Liouville problems with Carathéodory perturbed term ⋮ Degenerate resonances and their stability in two-dimensional systems with small negative divergence ⋮ An alternative approach to study bifurcation from a limit cycle in periodically perturbed autonomous systems ⋮ A periodic bifurcation problem depending on a random variable ⋮ Poincaré index and periodic solutions of perturbed autonomous systems ⋮ Sharp partial order and linear autonomous systems ⋮ A note on forced oscillations in differential equations with jumping nonlinearities

Cites Work

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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
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• Periodic solutions of 𝑥”+𝑐𝑥’+𝑔(𝑥)=𝜖𝑓(𝑡)
• Repeated Resonance and Homoclinic Bifurcation in a Periodically Forced Family of Oscillators
• Continuation Theorems for Periodic Perturbations of Autonomous Systems
• Small parameter perturbations of nonlinear periodic systems
• Periodic solutions for a class of singulary perturbated systems
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• On the continuation of periodic orbits
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