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

Yuxia Guo, Monica Musso, Shuangjie Peng, Shusen Yan

OAI: oai:purehost.bath.ac.uk:publications/0121e912-1053-45b9-96d2-78543c01efa9 • DOI: https://doi.org/10.1016/j.jfa.2020.108553

We consider the following prescribed scalar curvature equations in R^N −Δu=K(|y|)u^2⁎−1,u>0inR^N,u∈D^1,2(R^N), where K(r) is a positive function, [Formula presented]. 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.

Bubbling analysis Critical Sobolev exponent Non-degeneracy of entire solutions Pohozaev identity /dk/atira/pure/subjectarea/asjc/2600/2603 name=Analysis