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, xt), 0 < t < 1, x0 = 0, x(1) = 0, are obtained by applying the Schauder fixed-point theorem, where xt(u) = x(t+u) (0 ≤ t ≤ 1) on [-r, 0] and f(.,.) : (0, 1) × (C+\{0})→R+(C+ = {x ϵ C([-r, 0], R), x(t) ≥ 0, ∀t ϵ [-r, 0]}) may be singular at φ(u) = 0 (-r ≤ u ≤ 0) and t = 0. As an application, an example is given to demonstrate our result. [ABSTRACT FROM AUTHOR]