A new result on the existence of periodic solutions for Liénard equations with a singularity of repulsive type

In this paper, the problem of the existence of a periodic solution is studied for the second order differential equation with a singularity of repulsive type [Formula: see text] where [Formula: see text] is singular at [Formula: see text] , φ and h are T-periodic functions. By using the continuation theorem of Manásevich and Mawhin, a new result on the existence of positive periodic solution is obtained. It is interesting that the sign of the function [Formula: see text] is allowed to change for [Formula: see text] .