An extension of Dragilev's theorem for the existence of periodic solutions of the Liénard equation

DOI10.1016/j.na.2015.06.026zbMath1328.34026OpenAlexW884073476MaRDI QIDQ499613

Gabriele Villari, Martina Cioni

Publication date: 30 September 2015

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2158/903932

zbMATH Keywords

limit cycleDragilev theoremLienard equationwinding trajectory

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34)

Related Items (8)

An improved criterion for the unique existence of the limit cycle of a Liénard-type system with one parameter ⋮ Existence of harmonic solutions for some generalisation of the non-autonomous Liénard equations ⋮ On the uniqueness of the limit cycle for the Liénard equation with \(f(x)\) not sign-definite ⋮ Existence and non-existence of limit cycles for Liénard prescribed curvature equations ⋮ Remarks on a class of generalized Liénard planar systems ⋮ Periodic solutions of some autonomous Liénard equations with relativistic acceleration ⋮ Asymptotic behavior of periodic solutions in one-parameter families of Liénard equations ⋮ On the qualitative behavior of a class of generalized Liénard planar systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Extension of some results on forced nonlinear oscillations
• Periodic solutions of Lienard's equation
• Periodic solutions of the Liénard equation with one-sided growth restrictions
• On Massera's theorem concerning the uniqueness of a periodic solution for the Liénard equation. When does such a periodic solution actually exist?
• A general equation for relaxation oscillations
• More limit cycles than expected in Liénard equations
• On the existence of periodic solutions for Liénard's equation
• Liénard systems with several limit cycles
• Small-amplitude limit cycles of certain Liénard systems
• Relaxation oscillations
• Boundaries for the limit cycle of van der Pol’s equation
• On the non-uniqueness of periodic solutions for an asymmetric Liénard equation

This page was built for publication: An extension of Dragilev's theorem for the existence of periodic solutions of the Liénard equation