Ground state solution of critical biharmonic equation with Hardy potential and [formula omitted]-Laplacian

Abstract

In this paper, we consider the following critical biharmonic equation: Δ2u−Δpu−μu|x|4=|u|2∗−2u,inRN,where Δ2u=Δ(Δu), Δpu=div(|∇u|p−2∇u), N⩾5, p=2∗=2NN−2, 2∗=2NN−4 and μ∈(0,N2(N−4)216). By studying the non-vanishing of (PS)c sequence and the structure of (PS)c sequence going to zero weakly, we establish the existence of ground state solution to above equation. Our result extends previous results in the literature.