Positive solutions to superlinear semipositone periodic boundary value problems with repulsive weak singular forces *

This paper is devoted to study the existence of positive solutions to the second-order semipositone periodic boundary value problem x″ + a(t)x = f(t,x), x(0) = x(1), x′(0) = x′(1). Here, f (t, x) may be singular at x = 0 and may be superlinear at x = +∞. Our analysis relies on a fixed-point theorem in cones.