Multiplicity results for a boundary value problem with Dirichlet condition

In this paper, the existence of at least three weak solutions for the Dirichlet problem           = 0 , (| | ) ( , ) = ( ) | | , u on div u u f x u a x u u in where 2  R is non-empty bounded open set with smooth boundary  ,  > 0 , f :RR is a coninuous function and and positive weight function a(x)C() , is established. The approach is based on variational methods and critical points

Keywords:

Three solutions , Critical point , Multiplicity results , Dirichlet problem AMS subject classification: 35J20 , 34A15