Three solutions for a quasilinear two point boundary value problem involving the one-dimensional p-Laplacian

In this paper we prove the existence of at least three classical solutionsfor the problem\begin{equation*}\left\{\begin{array}{l}- \left( |u'|^{p-2} u' \right)' = \lambda f(t,u) h(u') \\u(a)=u(b)=0,\end{array}\right.\end{equation*}\noindent when $\lambda$ lies in an explicitly determined open interval.Our main tool is a very recent three critical points theorem statedin D.Averna, G.Bonanno, {\em A three critical point theoremand its applications to the ordinary Dirichlet problem}, Topol. Methods Nonlinear Anal., 22 (2003), p.93-104.