A BREZIS-NIRENBERG PROBLEM ON HYPERBOLIC SPACES

被引：0

作者：

Carriao, Paulo Cesar ^{[1
]}

Lehrer, Raquel ^{[2
]}

Miyagaki, Olimpio Hiroshi ^{[3
]}

Vicente, Andre ^{[2
]}

机构：

[1] Univ Fed Minas Gerais, ICEX, DM, BR-31270901 Belo Horizonte, MG, Brazil

[2] Univ Estadual Oeste Parana, CCET, Rua Univ,2069,Jd Univ, BR-85819110 Cascavel, PR, Brazil

[3] Univ Fed Juiz de Fora, DM, BR-36036330 Juiz De Fora, MG, Brazil

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2019年

关键词：

Variational method; critical point; critical exponent; hyperbolic manifold; SEMILINEAR ELLIPTIC EQUATION; R-N;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a Brezis-Nirenberg problem on the hyperbolic space H-n. By using the stereographic projection, the problem becomes a singular problem on the boundary of the open ball B-1 (0) subset of R-n. Thanks to the Hardy inequality, in a version due to Brezis-Marcus, the difficulty involving singularities can be overcame. We use the mountain pass theorem due to Ambrosetti-Rabinowitz and Brezis-Nirenberg arguments to obtain a nontrivial solution.

引用

页数：15

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