Exact multiplicity results for a class of two-point boundary value problems

This paper is concerned with the exact number of positive solutions for boundary value problems (|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 the nonlinearity f is positive on (0,∞) and (p −1)f (u)−uf (u) changes sign from negative to positive.  2005 Elsevier Inc. All rights reserved.