Multiple solutions for the fourth-order elliptic equation with vanishing potential

This paper is concerned with the following fourth-order elliptic equation Δ2u−Δu+V(x)u=K(x)f(u)+μξ(x)|u|p−2u,x∈RN,u∈H2(RN),where Δ2≔Δ(Δ) is the biharmonic operator, N≥5, V,K are nonnegative continuous functions and f is a continuous function with a quasicritical growth. By working in weighted Sobolev spaces and using a variational method, we prove that the above equation has two nontrivial solutions.