On the uniqueness of the limit cycle for the Liénard equation with \(f(x)\) not sign-definite

DOI10.1016/j.aml.2017.09.004zbMath1383.34054OpenAlexW2756238295MaRDI QIDQ1680040

Gabriele Villari, Fabio Zanolin

Publication date: 22 November 2017

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2017.09.004

zbMATH Keywords

uniquenesslimit cyclesLiénard equation

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

Related Items (6)

Existence and uniqueness of limit cycles in planar system of Liénard type ⋮ Existence of harmonic solutions for some generalisation of the non-autonomous Liénard equations ⋮ Limit cycles near a centre and a heteroclinic loop in a near-Hamiltonian differential system ⋮ Asymptotic behavior of periodic solutions in one-parameter families of Liénard equations ⋮ On the uniqueness of limit cycles in a generalized Liénard system ⋮ On the qualitative behavior of a class of generalized Liénard planar systems

Cites Work

• An extension of Dragilev's theorem for the existence of periodic solutions of the Liénard equation
• A note on existence and uniqueness of limit cycles for Liénard systems
• Qualitative analysis of the phase portrait for a class of planar vector fields via the comparison method
• Uniqueness of limit cycles for a class of planar vector fields
• Limit cycle uniqueness for a class of planar dynamical systems
• On Massera's theorem concerning the uniqueness of a periodic solution for the Liénard equation. When does such a periodic solution actually exist?
• Sopra l'equazione di A. Lienard delle oscillazioni di rilassamento
• A general equation for relaxation oscillations
• Van der Pol and the history of relaxation oscillations: Toward the emergence of a concept
• On the improved Massera’s theorem forthe unique existence of the limit cyclefor a Lienard equation
• On the uniqueness and nonexistence of limit cycles for predator prey systems
• On the non-uniqueness of periodic solutions for an asymmetric Liénard equation
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