Existence and multiplicity of nontrivial solutions for a class of modified nonlinear fourth-order elliptic equations on R N

In this paper, we study the following fourth-order elliptic equation of the form 2 u - u + V ( x ) u - 2 ( u 2 ) u = h ( x , u ) , x R N , where 2 ( ) is the biharmonic operator, 0 , N ≤ 6 , V C ( ...