Periodic solutions for Liénard equation with an indefinite singularity

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)xm(t)−α(t)xμ(t)=0,where f:(0,+∞)→R is a continuous function which may have a singularity at the origin, the signs of φ andα 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.