On Massera’s theorem concerning the uniqueness of a periodic solution for the Liénard equation. When does such a periodic solution actually exist?
Dipartimento di Matematica ‘U. Dini’, Università degli Studi di Firenze, viale Morgagni 67/A, Firenze, 50134, Italy
Boundary Value Problems 2013, 2013:144 doi:10.1186/1687-2770-2013-144Published: 11 June 2013
In this note we consider the classical Massera theorem, which proves the uniqueness of a periodic solution for the Liénard equation
and investigate the problem of the existence of such a periodic solution when f is monotone increasing for and monotone decreasing for but with a single zero, because in this case the existence is not granted. Sufficient conditions for the existence of a periodic solution and also a necessary condition, which proves that with this assumptions actually it is possible to have no periodic solutions, are presented.
MSC: 34C05, 34C25.