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
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
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页数:29
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