Abstract: By using the Krasnosel’skii fixed-point theorem, the author give the existence and multiplicity of positive solutions of a singular third-order three-point boundary value problem, in the case that both the weight function h(t) and the nonlinear term f(t,u) are singular, where a is positive constant, η∈［π/2,π), h: (0,π)→［0,+∞) and f: (0,π)×(0,∞)→［0,+∞) are continuous functions.

Key words: singularity, positive solution, multiplicity, third-order three-point boundary value problem