Monotone positive solutions for singular boundary value problems

Consider the nonlinear scalar differential equations 1/p(t)(p(t)y'(t))' + sign(1 - alpha)q(t)f(t, y(t), p(t)y'(t)) = 0, where alpha > 0, alpha not equal 1, p and q are "singular" at t = 0, 1 and f is an element of C((0, 1) x R+ x R-, R-), associated to boundary conditions gammay(0) + delta lim(t-->0+) p(t)y'(t) = 0, y > 0, lim(t-->1-) p(t)y'(t) = alpha lim(t-->0divided by) p(t)y'(t). Existence of a monotone positive solutions of this BVP are given, with their slope a priori bounded, under superlinear or sublinear growth in f. The approach is based on the analysis of the corresponding vector field on the face-plane and the well-known shooting technique. (C) 2002 Elsevier Science B.V. All rights reserved.