Periodic solutions of discontinuous damped Duffing equations. (June 2019)

• Record Type: Journal Article
• Authors: Jiang, Fangfang; Ji, Zhicheng; Wang, Yan
• Is Part Of: Nonlinear analysis. Volume 47(2019)
• Page Start: 484
• Page End: 495
• Publication Date: 2019-06
• Subjects: Discontinuity -- Damping -- Harmonic and subharmonic solutions -- Poincaré–Bohl theorem; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.11.009
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we are concerned with the problem of periodic solutions for a class of second order periodically forced nonlinear damped Duffing equations with a discontinuity line x ′ ′ + c x ′ + g ( x ) = e ( t ), where g ( x ) is discontinuous and e ∈ C 0 ( R, R ) is T -periodic. We first show that the periodic solutions can only be harmonic and subharmonic solutions. Secondly, note that g ( x ) is an abstract function, so the explicit solutions cannot be computed and then known theory cannot be applied directly. Therefore, we give geometric properties of solutions for the discontinuous forced damped Duffing equation. Then by the Poincaré–Bohl theorem we investigate the existence and uniqueness of crossing harmonic and subharmonic solutions of the equation.