Limit cycleʼs uniqueness for second order ODEʼs polynomial in

We prove a uniqueness result for limit cycles of the second order ODE x ¨ + ∑ j = 1 J f j ( x ) x ˙ j + g ( x ) = 0 . We extend a uniqueness result proved in Carletti, Rosati and Villari (2007) [2]. The main tool applied is an extension of the Massera theorem proved in Guillamon and Sabatini (2007) [5].