Non-radial solutions for higher order Hénon-type equation with critical exponent.

We consider the following polyharmonic equation with critical exponent (- Δ) m u = K (| y |) u m ∗ - 1 , u > 0 in B 1 (0) , u ∈ D 0 m , 2 (B 1 (0)) , <graphic href="30_2023_862_Article_Equ87.gif"></graphic> where m > 0 is a integer, m ∗ = : 2 N N - 2 m , B 1 (0) is the unit ball in R N , N ≥ 2 m + 4 , K : [ 0 , 1 ] → R N is a bounded function, K ′ (1) > 0 and K ′ ′ (1) exists. We prove a non-degeneracy result of the non-radial solutions constructed in Guo and Li (Calc Var PDEs 46(3–4):809–836, 2013) via the local Pohozaev identities for N ≥ 2 m + 4 . Then we apply the non-degeneracy result to obtain new existence of non-radial solutions for N ≥ 6 m . [ABSTRACT FROM AUTHOR]