Positive periodic solutions of second-order differential equations with weak singularities

We establish the existence of positive periodic solutions of the second-order differential equationu″+a(t)u=f(t,u)+c(t)u″+a(t)u=f(t,u)+c(t)via Schauder’s fixed point theorem, where a∈L1(R/TZ;R+),c∈L1(R/TZ;R),f is a Carathéodory function and is singular at u=0u=0. Our main results generalize some recent results by P.J. Torres.