Carriao, Paulo CesarLehrer, RaquelMiyagaki, Oliimpio HiroshiVicente, Andre2021-11-292021-11-292019-05-13Carrião, P. C., Lehrer, R., Miyagaki, O. H., & Vicente, A. (2019). A Brezis-Nirenberg problem on hyperbolic spaces. <i>Electronic Journal of Differential Equations, 2019</i>(67), pp. 1-15.1072-6691https://hdl.handle.net/10877/14955We 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.Text15 pages1 file (.pdf)enAttribution 4.0 InternationalVariational methodCritical pointCritical exponentHyperbolic manifoldArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.