On the uniqueness of the limit cycle for the Liénard equation with \(f(x)\) not sign-definite (Q1680040)

Consider the Liénard equation \[ \ddot x+ f(x)\dot x+ g(x)=0.\tag{\(*\)} \] The authors prove a theorem guaranteeing that \((*)\) has at most one limit cycle. The feature of their result consists in the fact that the classical assumption of sign-definiteness of \(f(x)\) is relaxed.