Nondegeneracy of the solutions for elliptic problem with critical exponent

This paper deals with the following nonlinear elliptic equation: − Δ u = Q ( | y ′ | , y ″ ) u N + 2 N − 2 , u > 0 , in R N , u ∈ D 1 , 2 ( R N ) , where ( y ′ , y ″ ) ∈ R 2 × R N − 2 , N ≥ 5 , Q ( | y ′ | , y ″ ) is a bounded nonnegative function in R 2 × R N − 2 . By using the local Pohozaev identities we prove a nondegeneracy result for the positive solutions constructed in (Peng et al. in J. Differ. Equ. 267:2503–2530, 2019 ).