Periodic solutions of Duffing equations with semi-quadratic potential and singularity

In this paper, we deal with the existence of periodic solutions of the second order differential equations x″+g(x)=p(t)x″+g(x)=p(t) with singularity. We prove that the given equation has at least one periodic solution when g(x)g(x) has singularity at origin, G(x)(=∫1xg(s)ds) satisfiesn24