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

Document Type : Research Paper


1 Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran

2 Department of Mathematics, Faculty of Basic Sciences, Payame Noor University, Tehran, Iran


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.