In this paper, we consider the H e ̵́ non equation { − ∆ u = | x | α u 2 ∗ − 1 + ϵ , u > 0 , in Ω , u = 0 , on ∂ Ω . where Ω is a bounded smooth domain in R N containing the origin, N≥3 and ϵ is a positive constant. M. Ben Ayed et.[2] proved the equation without | x | α doesn’t have the single peaked solution. Moreover, there are few works on the H e ̵́ non equation in a general domain. Inspired by them, we proved the non-existence of the single peak solution to the H e ̵́ non problem by Pohozaev identities.