Three Solutions to Dirichlet Boundary Value Problems for <inline-formula> <graphic file="1687-1847-2008-345916-i1.gif"/></inline-formula>-Laplacian Difference Equations

Abstract

We deal with Dirichlet boundary value problems for -Laplacian difference equations depending on a parameter . Under some assumptions, we verify the existence of at least three solutions when lies in two exactly determined open intervals respectively. Moreover, the norms of these solutions are uniformly bounded in respect to belonging to one of the two open intervals.