An extension of Dragilev's theorem for the existence of periodic solutions of the Liénard equation. (November 2015)

• Record Type: Journal Article
• Authors: Cioni, Martina; Villari, Gabriele
• Is Part Of: Nonlinear analysis. Volume 127(2015)
• Page Start: 55
• Page End: 70
• Publication Date: 2015-11
• Subjects: 34C05 -- 34C25 -- 34C15; Liénard equation -- Limit cycles -- Dragilev's theorem; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.06.026
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The problem of the existence of periodic solution for the Liénard equation is investigated, and a result which improves the classical Dragilev's theorem is presented, together with a corollary in which there are no assumptions on the function g ( x ), and hence on G ( x ), besides the standard sign condition. In the final part of the paper constructive examples with several limit cycles are provided.