The Nehari manifold for a Navier boundary value problem involving the p-biharmonic

Abstract

In this paper, we study the Nehari manifold and its application on the following Navier boundary valueproblem involving the p-biharmonic          0, on( ) 1 ( , ) , in , 2*2u uf x u u upu u p q where  is a bounded domain in RN with smooth boundary  . We prove that the problem has atleast two nontrivial nonnegtive solutions when the parameter  belongs to a certain subset of R .