Abstract: This paper investigates the existence of positive solutions for second-order singular sub-linear three-point boundary value problems. A necessary and sufficient condition for the existence of C [0,1] as well as C¹[0,1] positive solutions is given by constructing lower and upper solutions and with the comparison theorem. The nonlinearity f(t,x) may be singular at , \ t=0 and /or t=1 .

Key words: Singular three-point boundary value problem, Positive solution, Lower and upper solutions, Comparison theorem