Concentration for a bi-harmonic Schrödinger equation with critical nonlinearity

This paper concerns the following fourth-order problem{ϵ4Δ2u+V(x)u=P(x)(f(|u|)+|u|2⁎−2)u,x∈RN,u(x)→0as|x|→∞, where 2⁎=2NN−4, V and P   are spatial distributions of external potentials. By variational methods, the concentration phenomena of the solutions as ϵ→0ϵ→0 is considered.