Exact multiplicity results for a p-Laplacian positone problem with concave-convex-concave nonlinearities

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 satisfies $f(0)>0$ (positone) and has three distinct simple positive zeros and such that $f''$ changes sign exactly twice on $(0,infty)$. Note that we may allow $f''$ to change sign more than twice on $(0,infty )$. We also present some interesting examples.