Concentration on the Clifford torus for the critical problem in an annulus

Abstract

In this paper, we are concerned with the existence of solutions for the following critical elliptic problem:(P){−Δu=|u|4N−2u, in Ω,u=0, on ∂Ω. where Ω:={x∈RN:a<|x|<b} is an annulus, N≥5. By using a finite reduction argument, we prove the existence of infinitely many non-radial sign-changing solutions concentrating on the Clifford torus.