Intersection with the vertical isocline in the Liénard plane Original Research Article

In this paper, we study the problem of whether all trajectories of the Liénard system View the MathML sourceẋ=y−F(x) and View the MathML sourceẏ=−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.