6533b839fe1ef96bd12a6a87

RESEARCH PRODUCT

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

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In this paper we prove the existence of at least three classical solutions for 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 stated in D.Averna, G.Bonanno, {\em A three critical point theorem and its applications to the ordinary Dirichlet problem}, Topol. Methods Nonlinear Anal., 22 (2003), p.93-104.