In this paper we prove the existence of an open interval (λ ′ ,λ ′′) for each λ in the interval a class of Neumann boundary value equations involving the (p1,..., pn)- Laplacian and depending on λ admits at least three solutions. Our main tool is a recent three critical points theorem of Averna and Bonanno [Topol. Methods Nonlinear Anal. [1] (2003) 93-103].
