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

Abstract

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