In this note we consider the classical Massera theorem, which proves the uniquenessof a periodic solution for the Liénard equation x''+ f (x)x' + x = 0, and investigate the problem of the existence of such a periodic solution when f is monotone increasing for x > 0 and monotone decreasing for x < 0 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
On Massera’s theorem concerning the uniqueness of a periodic solution for the Liénard equation. When does such a periodic solution actually exist? / Rosati, Lilia; Villari, Gabriele. - In: BOUNDARY VALUE PROBLEMS. - ISSN 1687-2770. - ELETTRONICO. - (2013), pp. 0-0. [10.1186/1687-2770-2013-144]
On Massera’s theorem concerning the uniqueness of a periodic solution for the Liénard equation. When does such a periodic solution actually exist?
VILLARI, GABRIELE
2013
Abstract
In this note we consider the classical Massera theorem, which proves the uniquenessof a periodic solution for the Liénard equation x''+ f (x)x' + x = 0, and investigate the problem of the existence of such a periodic solution when f is monotone increasing for x > 0 and monotone decreasing for x < 0 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
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