Abstract
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.
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