We mainly study the existence of positive solutions for the following third order singular multi-point boundary value problem
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x(3)(t) + f(t, x(t), x′(t)) = 0, 0 < t < 1,
x(0) −∑m1i=1αix(ξi) = 0, x′(0) −∑m2i=1βix′(ηi) = 0, x′(1) = 0,
where 0 ≤αi ≤∑m1i=1αi < 1, i = 1, 2, …, m1, 0 < ξ1 < ξ2 < … < ξm1 < 1, 0 ≤βj ≤∑m2i=1βi <1, j = 1, 2, … , m2, 0 < η1 < η2 < … < ηm2 < 1. And we obtain some necessary and sufficient conditions for the existence of C1[0, 1] and C2[0, 1] positive solutions by constructing lower and upper solutions and by using the comparison theorem. Our nonlinearity f(t, x, y) may be singular at x, y, t = 0 and/or t = 1.
