Multiple positive solutions for nonlinear periodic problems

We consider a nonlinear periodic equation driven by the scalar pp-Laplacian and with a Caratheodory asymptotically (p−1)(p−1)-linear nonlinearity. Using variational methods coupled with suitable truncation techniques, we show that the problem has at least two positive solutions. For the semilinear case (p=2p=2), using Morse theory we show that the problem has three distinct positive solutions.