The story of the Massera Theorem, a striking result on the uniqueness of limit cycles for the Liénard equation, will be discussed, starting from the first version due to Giovanni Sansone. This result was proved in Florence, when Massera was visiting the former Institute of Mathematics, which at that time was located in via Alfani and only later moved to viale Morgagni in 1963. Its elegant and geometrical proof will be presented, as well as some generalizations.

Moreover, the talk will speak of the friendship between the two mathematicians and the effort of Sansone in order to save the life of his friend Massera, who, as a militant communist, was arrested in 1975 in Montevideo, after the military intervention in Uruguay of 1973. It will also be the occasion of presenting Sansone outstanding figure, the founder of Florence Mathematical school, to the younger generations of mathematicians an students.

[1] G. Sansone, Soluzioni periodiche dell'equazione di Liénard. Rend. Semin. Mat. Univ. Politec. Torino 10 (1951):154–171

[2] J.L. Massera, Sur un théorème de G. Sansone sur l'équation de Liénard. Boll. Unione Mat. Ital. 9:4 (1954):367–369

[3] G. Villari, An improvement of Massera's theorem for the existence and uniqueness of a periodic solution for the Liénard equation. Rend. Istit. Mat. Univ. Trieste 44 (2012):187–195

[4] L. Rosati, G. Villari, On Massera's theorem concerning the uniqueness of a periodic solution for the Liénard equation. When does such a periodic solution actually exist? Bound. Value Probl. (2013)144