Periodic solutions of some autonomous Liénard equations with relativistic acceleration

After giving a new proof of the existence of a stable limit cycle for the relativistic Van der Pol equation ddtẋ1−ẋ2+k(x2−1)ẋ+x=0,we find sufficient conditions upon f and g in order that the relativistic Liénard equation ddtẋ1−ẋ2+f(x)ẋ+g(x)=0has a stable limit cycle. The approach and the existence conditions are distinct from those recently obtained by Pérez-González et al. (2016).