Electron. J. Differential Equations, Vol. 2021 (2021), No. 53, pp. 1-12.

Kirchhoff-type problems with critical Sobolev exponent in a hyperbolic space

Paulo Cesar Carriao, Augusto Cesar dos Reis Costa, Olimpio Hiroshi Miyagaki, Andre Vicente

In 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.

Submitted January 30, 2021. Published June 14, 2021.
Math Subject Classifications: 58J05, 35R01, 35J60, 35B33.
Key Words: Kirchhoff-type problem; variational methods; hyperbolic space.

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Paulo Cesar Carrião
Departamento de Matemática
Universidade Federal de Minas Gerais
Belo Horizonte, MG 31270-901, Brazil
email: pauloceca@gmail.com
Augusto César dos Reis Costa
Faculdade de Matemática
Instituto de Ciências Exatas e Naturais
Universidade Federal do Pará
Belém, PA 66075-110, Brazil
email: aug@ufpa.br
Olimpio Hiroshi Miyagaki
Departamento de Matemática
Universidade Federal de Juiz de Fora
Juiz de Fora, MG 36036-330, Brazil
email: ohmiyagaki@gmail.com
André Vicente
Centro de Ciências Exatas e Tecnolóogicas
Universidade Estadual do Oeste do Paraná,
Cascavel, PR 85819-110, Brazil
email: andre.vicente@unioeste.br

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