Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 4 2 2013 10 01 Existence of three positive solutions for nonsmooth functional involving the p-biharmonic operator 68 77 57 10.22075/ijnaa.2013.57 EN M. B. Ghaemi Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran S. Mir Department of Mathematics, Faculty of Basic Sciences, Payame Noor University, Tehran, Iran Journal Article 2012 01 01 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. https://ijnaa.semnan.ac.ir/article_57_5995deabc4ef72cb8b950293b0826ecc.pdf