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On the prescribed scalar curvature problem with very degenerate prescribed functions

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成果类型:
期刊论文
作者:
Luo, Peng;Peng, Shuangjie;Zhou, Yang
通讯作者:
Peng Luo
作者机构:
[Luo, Peng; Zhou, Yang; Peng, Shuangjie] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
[Luo, Peng; Peng, Shuangjie] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构:
[Peng Luo] S
School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, China
语种:
英文
关键词:
35A01;35B25;35J20;35J60
期刊:
Calculus of Variations and Partial Differential Equations
ISSN:
0944-2669
年:
2023
卷:
62
期:
3
页码:
1-35
基金类别:
Peng Luo and Shuangjie Peng were supported by NSFC Grants (No. 11831009) and the Fundamental Research Funds for the Central Universities (No. CCNU22LJ002). Peng Luo was partially supported by NSFC Grants (No. 12171183) and the Fundamental Research Funds for the Central Universities (No. KJ02072020-0319).
机构署名:
本校为第一机构
院系归属:
数学与统计学学院
摘要:
We revisit the well known prescribed scalar curvature problem $$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u=\big (1+\varepsilon K(x)\big )u^{2^*-1}, u(x)>0,~~ &{}{x\in \mathbb {R}^N},\\ u\in \mathcal {D}^{1,2}(\mathbb {R}^N),\\ \end{array}\right. } \end{aligned}$$ where $$2^*=\frac{2N}{N-2}$$ , $$N\ge 5$$ , $$\varepsilon >0$$ and $$K(x)\in C^1(\mathbb {R}^N)\cap L^{\infty }(\mathbb {R}^N)$$ . It is known that there are a number of results related to the existence of solutions conce...

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