Periodic solutions for Liénard equation with an indefinite singularity. (February 2019) - Lu, Shiping; Guo, Yuanzhi; Chen, Lijuan
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.