Intersection with the vertical isocline in the Liénard plane

✍ Scribed by A. Aghajani; A. Moradifam

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 271 KB
• Volume: 68
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2007.03.040

✦ Synopsis

In this paper, we study the problem of whether all trajectories of the Liénard system ẋ = y -F(x) and ẏ = -g(x) cross the vertical isocline, which is very important for the existence of periodic solutions and oscillation theory. We solve this problem completely in some sense. Our results include a proof for an old conjecture of Hara and Sugie.