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 (Pλ) depending on a positive parameter λ. By a variational method, we prove that for every λ>1 problem (Pλ) has at least two non-zero solutions, while there exists λˆ>1 such that problem (Pλˆ) has at least three non-zero solutions.