A unified approach to periodic solutions for a class of non-autonomous second order Hamiltonian systems. (April 2021)

• Record Type: Journal Article
• Authors: Wang, Zhiyong; Zhang, Jihui; Chen, Mengxi
• Is Part Of: Nonlinear analysis. Volume 58(2021)
• Publication Date: 2021-04
• Subjects: Control functions -- Periodic solutions -- Minimax methods; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103218
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is dedicated to studying the periodic solutions of non-autonomous second order Hamiltonian systems. By virtue of control functions and the minimax methods in critical point theory, we propose a unified approach when the nonlinearity is unbounded while grows no more than | x | at infinity. We establish some new existence theorems on periodic solutions, which unify and generalize many previously known results in the literature.