Three non-zero solutions for a nonlinear eigenvalue problem

In the present paper we prove a novel multiplicity result for a model quasilinear Dirichlet problem ( P λ ) depending on a positive parameter λ . By a variational method, we prove that for every λ > 1 problem ( P λ ) has at least two non-zero solutions, while there exists λ ˆ > 1 such that problem ( P λ ˆ ) has at least three non-zero solutions.