A nonlinear eigenvalue problem for the periodic scalar p-Laplacian

We study a parametric nonlinear periodic problem driven by the scalar p-Laplacian. We show that if $\hat\lambda_1> 0$ is the first eigenvalue of the periodic scalar p-Laplacian and $\lambda>\hat\lambda_1$, then the problem has at least three nontrivial solutions one positive, one negative and the third nodal. Our approach is variational together with suitable truncation, perturbation and comparison techniques.