Existence-uniqueness results for a class of singular boundary value problems-II

In this paper we establish existence-uniqueness of solution of a class of singular boundary value problem −(p(x)y (x)) = q(x)f (x, y) for 0 < x b and y(0) = a, α1y(b) + β1y (b) = γ1, where p(x) satisfies (i) p(x) > 0 in (0, b), (ii) p(x) ∈ C1(0, r), and for some r >b, (iii) x p (x) p(x) is analytic in {z: |z| < r} and q(x) satisfies (i) q(x)>0 in (0, b), (ii) q(x) ∈ L1(0, b) and for some r >b, (iii) x2 q(x) p(x) is analytic in {z: |z| < r} with quite general conditions on f (x, y). Region for multiple solutions have also been determined. © 2007 Elsevier Inc. All rights reserved.