Nonlinear periodic problems with a jumping reaction

We consider a periodic problem driven by the scalar $p-$Laplacian and with a jumping (asymmetric) reaction. We prove two multiplicity theorems. The first concerns the nonlinear problem ($1<p<\infty$) and produces two nontrivial solutions. The second is for the semilinear problem ($p=2$) and produces three solutions. The tools of our analysis are variational and Morse theoretic.