Abstract

We study existence and uniqueness of positive solutions of the boundary value problem (P)lambda {- (\u'\(m-2)u')' = lambdaf(u) in (0, 1), u(0) = u(1) = 0, where lambda is a positive parameter, m > 1, and f : [0, + infinity) --> R is a continuous function which vanishes at most once in (0, + infinity). Assuming that f is superlinear at + infinity, we study its behavior near zero to obtain uniqueness results, which are proved using the shooting method. (C) 2003 Elsevier Science Ltd. All rights reserved.