Multiplicity positive solutions to superlinear repulsive singular second order impulsive differential equations

In this paper, we study positive periodic solutions to the repulsive singular perturbation Hill equations with impulse effects. It is proved that such a perturbation problem has at least two positive impulsive periodic solutions when the anti-maximum principle holds for the Hill operator and the perturbation is superlinear at infinity. The proof relies on a nonlinear alternative of Leray-Schauder type and on Krasnoselskii fixed point theorem on compression and expansion of cones.