On a continuation lemma for the study of a certain planar system with applications to Liénard and Rayleigh equations

DOI10.1007/BF03323223zbMath0661.34034WikidataQ124843204 ScholiaQ124843204MaRDI QIDQ1112994

Gabriele Villari, Pierpaolo Omari

Publication date: 1988

Published in: Results in Mathematics (Search for Journal in Brave)

zbMATH Keywords

Liénard equationplanar systemcontinuation lemmaRayleigh equation

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Periodic solutions to ordinary differential equations (34C25)

Related Items

Periodic solutions of Rayleigh equations with singularities ⋮ Periodic solutions of some second-order differential equations with desultorily sublinear nonlinearities ⋮ Periodic solutions of Rayleigh equations via time-maps ⋮ A continuation lemma and its applications to periodic solutions of Rayleigh differential equations with subquadratic potential conditions ⋮ Boundedness of solutions and existence of limit cycles for a nonlinear system ⋮ Global exponential stability of a discrete-time Rayleigh system with delays ⋮ Remarks on a class of generalized Liénard planar systems ⋮ Periodic solutions of Liénard equations with superlinear asymmetric nonlinearities. ⋮ A geometric approach to periodically forced dynamical systems in presence of a separatrix

Cites Work

• On the ranges of certain damped nonlinear differential equations
• Periodic solutions of some forced Liénard differential equations at resonance
• Periodic solutions of a second-order differential equation with one-sided growth restrictions on the restoring term
• Periodic solutions of a differential delay equation of Rayleigh type
• Periodic solutions for second order differential systems with damping
• Expension of some results concerning the generalized Lienard equation
• Schwingungssätze für die verallgemeinerte Lienardsche Differentialgleichung
• Periodic solutions of a second order differential equation including a onesided restoring term
• Periodic solutions of the Liénard equation with one-sided growth restrictions
• On Schauder's fixed point theorem and forced second-order nonlinear oscillations
• An extension of a theorem of A. C. Lazer on forced nonlinear oscillations
• On the generalized Lienard equation with negative damping
• Periodic solutions of forced Liénard equations with jumping nonlinearities under nonuniform conditions
• Necessary and Sufficient Conditions for the Continuability of Solutions of the System
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item