High energy solutions of modified quasilinear fourth-order elliptic equations with sign-changing potential

In the present paper, we consider the following modified quasilinear fourth-order elliptic equation (1.1){Δ2u−Δu+V(x)u−12Δ(u2)u=f(x,u),forx∈RN,u(x)∈H2(RN), where Δ2:=Δ(Δ) is the biharmonic operator, V∈C(RN,R) and f∈C(RN×R,R), N≤5, are allowed to be sign-changing. Two main theorems on the existence of nontrivial solutions and infinitely many high energy solutions for Eq. (1.1) are obtained via variational methods.