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

摘要

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 ≤ b are 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).