Positive Solutions of Singular Initial-Boundary Value Problems to Second-Order Functional Differential Equations

Positive solutions to the singular initial- boundary value problems x '' = -f(t, x(t)), 0 < t < 1, x(0) = 0, x(1) = 0, are obtained by applying the Schauder fixed-point theorem, where x(t)(u) = x(t + u) (0 <= t <= 1) on [- r, 0] and f(.,.) : (0, 1) x (C+\{0}) -> R+(C+ = {x is an element of C ([-r, 0], R), x(t) >= 0, for all t is an element of [-r, 0]}) may be singular at. phi(u) = 0(-r <= u <= 0) and t = 0. As an application, an example is given to demonstrate our result. Copyright (C) 2008 F. Jin and B. Yan.