Abstract: This paper deals with the multiplicity of positive solutions to singular superlinear equations with periodic boundary value problems. It is proved that such a problem has at least two positive solutions under our r easonable conditions when the nonlinear term possesses singularity and super-linearity. The proof relies on a nonlinear alternative of LeraySchauder theorem and Krasnoselskii on fixed point theorem in cones.

Key words: periodic boundary value problem, singular superlinear equation, periodic solution, LearaySchauder alternative theorem, Krasnoselski i fixed point theorem in cones