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A class of critical Kirchhoff problem on the hyperbolic space \(\mathbb{H}^n\). (English) Zbl 1435.58002

The authors study a class of critical Kirchhoff-type problems in the hyperbolic space. The existence of a nontrivial solution is obtained by the use of a version of the Hardy inequality, due to Brezis-Marcus and the mountain pass theorem due to Ambrosetti-Rabinowitz.

MSC:

58J05 Elliptic equations on manifolds, general theory
35R01 PDEs on manifolds
35J60 Nonlinear elliptic equations
35B33 Critical exponents in context of PDEs
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