Existence of nontrivial solutions for a biharmonic equation with p-Laplacian and singular sign-changing potential

In the paper, we study a class of biharmonic equations with p-Laplacian and singular sign-changing potential as follows: Δ2u−βΔpu+Vλ(x)u=0 in RN,u∈H2(RN),where N≥5, β<0, Δpu=div(|∇u|p−2∇u) with p≥2 and Vλ(x)=λa(x)−b(x) with λ>0. Under some suitable assumptions on a and b, we obtain the existence of nontrivial solutions for λ large enough.