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Constructing solutions for the prescribed scalar curvature problem via local Pohozaev identities

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成果类型:
期刊论文
作者:
Peng, Shuangjie*;Wang, Chunhua;Wei, Suting
通讯作者:
Peng, Shuangjie
作者机构:
[Peng, Shuangjie] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.
通讯机构:
[Peng, Shuangjie] C
Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
语种:
英文
期刊:
Journal of Differential Equations
ISSN:
0022-0396
年:
2019
卷:
267
期:
4
页码:
2503-2530
基金类别:
NSFCNational Natural Science Foundation of China (NSFC) [11831009, 11571130, 11671162]; excellent doctorial dissertation cultivation grant from Central China Normal University [2018YBZZ070]; [CCNU18CXTD04]
机构署名:
本校为第一且通讯机构
院系归属:
数学与统计学学院
摘要:
This paper deals with the following prescribed scalar curvature problem -Delta u = Q(vertical bar y'vertical bar, y '')u(N+2/N-2), u > 0, y = (y',y '') is an element of R-2 x RN-2, where Q(y) is nonnegative and bounded. By combining a finite reduction argument and local Pohozaev type of identities, we prove that if N >= 5 and Q(r, y '') has a stable critical point (r(0), y(0)'') with r(0) > 0 and Q(r(0), y(0)'') > 0, then the above problem has infinitely many solutions, whose energy can be made arbitrarily large. Here, instead of estimating directly the derivatives of the reduced functional, w...

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