A necessary and sufficient condition for the existence of positive solutions to singular sublinear three-point boundary value problems

This paper investigates the existence of positive solutions for second-order singular sublinear 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 maximal theorem. Also, the uniqueness, iterative methods, convergence rate and computational methods of the C1[0, 1] positive solutions are studied. Our nonlinear term may be singular at t = 0 and/or t = 1.