On an Elliptic Problem with Critical Nonlinearity in Expanding Annuli

This paper is concerned with an elliptic problem with homogeneous boundary conditions and critical nonlinearity (Pε): −Δu=up,u>0 onAε,u=0 on ∂Aε, whereAε={x∈Rn/ε<|x|<1/ε} are expanding annuli asε→0,n⩾3 andp+1=2n/(n−2) is the critical Sobolev exponent. We compute the difference of topology induced by the critical points at infinity between the level sets of the functional corresponding to (Pε) forεsmall enough.