Exact number of positive solutions for semipositone problems ✩

This paper is concerned with the exact number of positive solutions for the boundary value problem (|y |p−2y ) + λf (y) = 0 and y(−1) = y(1) = 0, where p > 1 and λ > 0 is a positive parameter. We consider the case in which both f (u) and g(u) = (p − 1)f (u) − uf (u) change sign exactly once from negative to positive on (0,∞).  2005 Elsevier Inc. All rights reserved