Periodic solutions for Liénard equation with an indefinite singularity. (February 2019)

• Record Type: Journal Article
• Authors: Lu, Shiping; Guo, Yuanzhi; Chen, Lijuan
• Is Part Of: Nonlinear analysis. Volume 45(2019)
• Page Start: 542
• Page End: 556
• Publication Date: 2019-02
• Subjects: Liénard equation -- Continuation theorem -- Periodic solution -- Singularity; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.07.024
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, the problem of periodic solutions is studied for Liénard equations with anindefinite singularity x ′ ′ ( t ) + f ( x ( t ) ) x ′ ( t ) + φ ( t ) x m ( t ) − α ( t ) x μ ( t ) = 0, where f : ( 0, + ∞ ) → R is a continuous function which may have a singularity at the origin, the signs of φ and α are allowed to change, m is a non-negative constant, and μ is a positive constant. The approach is based on a continuation theorem of Manásevich and Mawhin with techniques of a priori estimates. The main results partly answer the open problem proposed by R. Hakl, P.J. Torres and M. Zamora in the known literature.