Three solutions for a mixed boundary value problem involving the one-dimensional p-Laplacian ✩

This paper deals with two mixed nonlinear boundary value problems depending on a parameter λ. For each of them we prove the existence of at least three generalized solutions when λ lies in an exactly determined open interval. Usefulness of this information on the interval is then emphasized by means of some consequences. Our main tool is a very recent three critical points theorem stated in [Topol. Methods Nonlinear Anal. 22 (2003) 93–104].  2004 Elsevier Inc. All rights reserved.