Multiple positive solutions for nonlinear periodic problems

Abstract

We consider a nonlinear periodic equation driven by the scalar p -Laplacian and with a Caratheodory asymptotically ( 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 = 2 ), using Morse theory we show that the problem has three distinct positive solutions.