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.


Volume 4, Issue 2 - Serial Number 2
October 2013
Pages 68-77
  • Receive Date: 01 January 2012
  • Revise Date: 08 June 2013
  • Accept Date: 14 June 2013