Existence of three positive solutions for nonsmooth functional involving the p-biharmonic operator

This paper is concerned with the study of the existence of positive solutions for a Navier boundary value problem involving the p-biharmonic operator; the right hand side of problem is a nonsmooth functional with variable parameters. The existence of at least three positive solutions is established by using nonsmooth version of a three critical points theorem for discontinuous functions. Our results also yield an estimate on the norms of the solutions indepent of the parameters.