Carriao, Paulo CesarCosta, Augusto Cesar dos ReisMiyagaki, Olimpio H.Vicente, Andre2021-08-272021-08-272021-06-14Carrião, P. C., Costa, A. C. D. R., Miyagaki, O. H., & Vicente, A. (2021). Kirchhoff-type problems with critical Sobolev exponent in a hyperbolic space. Electronic Journal of Differential Equations, 2021(53), pp. 1-12.1072-6691https://hdl.handle.net/10877/14463In this work we study a class of the critical Kirchhoff-type problems in a Hyperbolic space. Because of the Kirchhoff term, the nonlinearity uq becomes concave for 2 < q < 4. This brings difficulties when proving the boundedness of Palais Smale sequences. We overcome this difficulty by using a scaled functional related with a Pohozaev manifold. In addition, we need to overcome singularities on the unit sphere, so that we use variational methods to obtain our results.Text12 pages1 file (.pdf)enAttribution 4.0 InternationalKirchhoff-type problemVariational methodsHyperbolic spaceArticle