The existence of positive solutions to a non-local singular boundary value problem

We consider the non-local singular boundary value problem [GRAPHICS] where q epsilon C-0( 0,1]) and f, h epsilon C-0((0, infinity)), lim(x -> 0+) f (x) = - infinity, lim(x -> 0+) h(x) = infinity. We present conditions guaranteeing the existence of a solution x epsilon C-1([0, 1]) boolean AND C-2((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 (c) 2005 John Wiley & Sons, Ltd.