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

Document Type: Regular Paper

Author

Department of Mathematics, Faculty of Sciences Razi University, 67149 Kermanshah, Iran

Abstract

In this paper, we study the Nehari manifold and its application on the following Navier boundary value
problem involving the p-biharmonic



   
       
0, on
( ) 1 ( , ) , in , 2
*
2
u u
f x u u u
p
u u p q 
where  is a bounded domain in RN with smooth boundary  . We prove that the problem has at
least two nontrivial nonnegtive solutions when the parameter  belongs to a certain subset of R .

Keywords