Nondegeneracy of the solutions for elliptic problem with critical exponent

This paper deals with the following nonlinear elliptic equation: -Δ u=Q(|y'|,y'')uN+2/N-2,\,\,u>0,\,\,in\, RN,\,\,u∈ D1,2(RN), where (y',y'')∈ R²× RN-2 , N≥ 5 , $Q(|y'|,y'')$ is a bounded nonnegative function in R²× RN-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).