Existence and multiplicity of solutions for a class of fourth-order elliptic equations in

In this paper, we study the existence and multiplicity of nontrivial solutions for the following fourth-order elliptic equations { △ 2 u − △ u + λ V ( x ) u = f ( x , u ) , in  R N u ∈ H 2 ( R N ) . via variational methods. Two main theorems are obtained.