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We consider the existence of positive solutions of the equation $1/\lambda \left(t\right){\left(\lambda \left(t\right){\phi }_p\left(x^{\text{'}}\left(t\right)\right)\right)}^{\text{'}}+\mu f(t,x\left(t\right),x^{\text{'}}\left(t\right))=0$, where ${\phi }_p\left(s\right)={\left|s\right|}^{p-2}s$, p > 1, subject to some singular Sturm-Liouville boundary conditions. Using the Krasnosel’skiĭ fixed point theorem for operators on cones, we prove the existence of positive solutions under some structure conditions.