Conditions for approaching the origin without intersecting the x-axis in the Liénard plane

DOI10.2298/FIL1712761AzbMath1488.34218MaRDI QIDQ5162032

Asadollah Aghajani, Mohsen Mirafzal, Donal O'Regan

Publication date: 1 November 2021

Published in: Filomat (Search for Journal in Brave)

zbMATH Keywords

Liénard systemoscillationlimit cyclehomoclinic orbit

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) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Homoclinic orbits for the planar system of Liénard-type
• Oscillations for Liénard type equations
• Intersection with the vertical isocline in the Liénard plane
• Oscillation theorems for nonlinear differential equations of second order
• Oscillation of solutions of second-order nonlinear self-adjoint differential equations
• Existence and non-existence of homoclinic trajectories of the Liénard system
• On the homoclinic orbits of the generalized Liénard equations
• New conditions for the intersection of orbits with the vertical isocline of the Liénard system
• Sufficient conditions for the intersection of orbits with the vertical isocline of the Liénard system
• Non-oscillation of half-linear differential equations with periodic coefficients
• THE GENERALISED LIÉNARD EQUATIONS
• Notice on the Vinograd type theorems for Liénard system
• Nonlinear oscillations of second order differential equations of Euler type
• Boundedness and oscillation of solutions of the Liénard equation

This page was built for publication: Conditions for approaching the origin without intersecting the x-axis in the Liénard plane