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Multiplicity positive solutions to superlinear repulsive singular differential equations with impulse effects

In this paper, we study positive 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. The proof relies on a nonlinear alternative of Leray-Schauder type and on Krasnoselskii fixed point theorem on compression and expansion of cones, Our results generalize the results presented in [1].