Abstract: | We consider the non‐local singular boundary value problem (1) where q ∈ C0(0,1]) and f, h ∈ C0((0,∞)), limf(x)=?∞, limh(x)=∞. We present conditions guaranteeing the existence of a solution x ∈ C1(0,1]) ∩ C2((0,1]) which is positive on (0,1]. The proof of the existence result is based on regularization and sequential techniques and on a non‐linear alternative of Leray–Schauder type. Copyright © 2005 John Wiley & Sons, Ltd. |