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

被引：36

作者：

Guo, Yuxia ^{[1
]}

Musso, Monica ^{[2
]}

Peng, Shuangjie ^{[3
]}

Yan, Shusen ^{[3
]}

机构：

[1] Tsinghua Univ, Dept Math, Beijing 100084, Peoples R China

[2] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

[3] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2020年 / 279卷 / 06期

基金：

英国工程与自然科学研究理事会;

关键词：

Pohozaev identity; Bubbling analysis; Non-degeneracy of entire solutions; Critical Sobolev exponent; DELTA-U; S-N; PERTURBATION; UNIQUENESS;

D O I：

10.1016/j.jfa.2020.108553

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the following prescribed scalar curvature equations in R-N -Delta u = K(vertical bar y vertical bar)u(2)*(-1), u > 0 in R-N, u is an element of D-1,D-2(R-N), (0.1) where K(r) is a positive function, 2* = 2N/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. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：29

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