On a class of weakly regular singular two-point boundary value problems .2.

Existence of a unique solution of a class of weakly regular singular two point boundary value problems -(p(x) y')' = p(x)f(x, y), 0 < x less than or equal to b, lim(x --> 0+) y'(x) = 0, y(b) = B, has been established, where p(x) satisfies: (i) p(x) > 0 on (0, b); (ii) p(x) is an element of C-1(0, r), and for some r > b; (iii) xp'(x)/p(x) is analytic in {z: \z\ < r} with Taylor expansion xp'(x)/p(x) = b(0) + b(1)x + ..., b(0) is an element of [0, 1) and with quite general conditions on f(x, v). These conditions on f(x, y) are sharp, which is seen through one example. Regions for multiple solutions have also been determined. (C) 1996 Academic Press, Inc.