Positive solutions for a class of singular semipositone boundary value problems

The paper presents sufficient conditions for the existence of positive solutions to the singular boundary value problem x " = muq(t)f(t, x, x'), alphax(0) - betax'(0) = a > 0, x(T) = 0 with q > 0 on (0, T), f greater than or equal to 0 on a suitable subset of [0, T] x (0, infinity) x R which may be singular at x = 0 and where either alpha, beta is an element of (0, infinity) or alpha = 0, beta = 1. Proofs are based on regularity and sequential techniques. (C) 2001 Elsevier Science Ltd. All rights reserved.