1. A BREZIS-NIRENBERG PROBLEM ON HYPERBOLIC SPACES.
- Author
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CARRIÃO, PAULO CÉSAR, LEHRER, RAQUEL, MIYAGAKI, OLÍMPIO HIROSHI, and VICENTE, ANDRÉ
- Subjects
- *
MOUNTAIN pass theorem , *SPHERICAL projection , *HYPERBOLIC spaces , *CRITICAL exponents - Abstract
We consider a Brezis-Nirenberg problem on the hyperbolic space Hn. By using the stereographic projection, the problem becomes a singular problem on the boundary of the open ball B1(0) ⊂ Rn. 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. [ABSTRACT FROM AUTHOR]
- Published
- 2019