Non-degeneracy of multi-bubbling solutions for the prescribed scalar curvature equations and applications

Abstract We consider the following prescribed scalar curvature equations in R N (0.1) − Δ u = K ( | y | ) u 2 ⁎ − 1 , u > 0 in R N , u ∈ D 1 , 2 ( R N ) , where K ( r ) is a positive function, 2 ⁎ = 2 N N − 2 . We first prove a non-degeneracy result for the positive multi-bubbling solutions constructed in [26] by using the local Pohozaev identities. Then we use this non-degeneracy result to glue together bubbles with different concentration rate to obtain new solutions.