Periodic solutions of some autonomous Liénard equations with relativistic acceleration. (September 2017)

• Record Type: Journal Article
• Authors: Mawhin, Jean; Villari, Gabriele
• Is Part Of: Nonlinear analysis. Volume 160(2017)
• Page Start: 16
• Page End: 24
• Publication Date: 2017-09
• Subjects: 34C05 -- 34C15 -- 34C35; Periodic orbits -- Limit cycles -- Van der Pol relativistic equation -- Liénard relativistic equation; 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.2017.05.001
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: After giving a new proof of the existence of a stable limit cycle for the relativistic Van der Pol equation d d t x ̇ 1 − x ̇ 2 + k ( x 2 − 1 ) x ̇ + x = 0, we find sufficient conditions upon f and g in order that the relativistic Liénard equation d d t x ̇ 1 − x ̇ 2 + f ( x ) x ̇ + g ( x ) = 0 has a stable limit cycle. The approach and the existence conditions are distinct from those recently obtained by Pérez-González et al. (2016).