Abstract
We study the exact number of positive solutions of a two-point Dirichlet boundary-value problem involving the p-Laplacian operator. We consider the case p = 2 and the case p > 1, when the nonlinearity f satisfies f(0) > 0 (positone) and has three distinct simple positive zeros and such that f″ changes sign exactly twice on (0, ∞). Note that we may allow f″ to change sign more than twice on (0, ∞). We also present some interesting examples.