Asymptotic behavior of periodic solutions in one-parameter families of Liénard equations. (January 2020)

• Record Type: Journal Article
• Authors: Cardin, Pedro Toniol; Novaes, Douglas Duarte
• Is Part Of: Nonlinear analysis. Volume 190(2020)
• Publication Date: 2020-01
• Subjects: primary 34C07 34C25 34C26 34C29 34D15; Liénard equation -- Limit cycles -- Relaxation oscillation theory -- Averaging theory; 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.2019.111617
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we consider one-parameter ( λ > 0 ) families of Liénard differential equations. We are concerned with the study on the asymptotic behavior of periodic solutions for small and large values of λ > 0 . To prove our main result we use the relaxation oscillation theory and a topological version of the averaging theory. More specifically, the first one is appropriate for studying the periodic solutions for large values of λ and the second one for small values of λ . In particular, our hypotheses allow us to establish a link between these two theories.