Kirchhoff-type problems with critical Sobolev exponent in a hyperbolic space
Date
2021-06-14
Authors
Carriao, Paulo Cesar
Costa, Augusto Cesar dos Reis
Miyagaki, Olimpio H.
Vicente, Andre
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
Kirchhoff-type problem, Variational methods, Hyperbolic space
Citation
Carrião, P. C., Costa, A. C. D. R., Miyagaki, O. H., & Vicente, A. (2021). Kirchhoff-type problems with critical Sobolev exponent in a hyperbolic space. <i>Electronic Journal of Differential Equations, 2021</i>(53), pp. 1-12.
Rights
Attribution 4.0 International