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

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.