Periodic solutions of some autonomous Liénard equations with relativistic acceleration (Q2011500)

Consider the relativistic Liénard equation \[ {d\over dt} {\dot x\over \sqrt{1-\dot x^2}}+ f(x)\dot x+ g(x)= 0.\tag{\(*\)} \] The authors derive conditions on the functions \(f\) and \(g\) such that \((*)\) has at least one stable limit cycle. The proof is based on the application of the Poincaré-Bendixson theorem. The approach and the existence conditions are distinct from those recently obtained by \textit{S. Pérez-González} et al. [J. Math. Anal. Appl. 439, No. 2, 745--765 (2016; Zbl 1346.34027)].