Abstract

We study the exact number of solutions of the quasilinear Neumann boundary-value problem (phi(p)(u'(t)))' + g(u(t)) = h(t) in (a, b), u'(a) = u'(b) = 0, where phi(p)(s) = vertical bar s vertical bar(p-2)s denotes the one-dimensional p-Laplacian. Under appropriate hypotheses on g and h, we obtain existence, multiplicity, exactness and non existence results. The existence of solutions is proved using the method of upper and lower solutions.