Periodic solutions for second order differential inclusions with the scalar p-Laplacian ✩

We study periodic problems driven by the scalar p-Laplacian with a multivalued right-hand side nonlinearity. We prove two existence theorems. In the first, we assume nonuniform nonresonance conditions between two successive eigenvalues of the negative p-Laplacian with periodic boundary conditions. In the second, we employ certain Landesman–Lazer type conditions. Our approach is based on degree theory. © 2005 Elsevier Inc. All rights reserved.