On boundary value problems for singular second-order functional differential equations

Positive solutions to the boundary value problem,y″=−f(x,y(w(x))), 0<x<1,αy(x)−βy′(x)=ξ(x), a⩽x⩽0,γy(x)+δy′(x)=η(x), 1⩽x⩽bare obtained by applying the Schauder fixed point theorem, where w(x) is a continuous function defined on [0,1] and f(x,y) is a function defined on (0,1)×(0,∞), which satisfies certain restrictions and may have singularity at y=0. The result corrects and improves an existence theorem due to Erbe and Kong (J. Comput. Appl. Math. 53 (1994) 377–388).