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A CLASS OF CRITICAL KIRCHHOFF PROBLEM ON THE HYPERBOLIC SPACE 
$\mathbb{H}^{{\it n}}$
Part of:
Miscellaneous topics - Partial differential equations
Partial differential equations
Elliptic equations and systems
Partial differential equations on manifolds; differential operators
Published online by Cambridge University Press: 21 January 2019
Abstract
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We investigate questions on the existence of nontrivial solution for a class of the critical Kirchhoff-type problems in Hyperbolic space. By the use of the stereographic projection the problem becomes a singular problem on the boundary of the open ball 
$B_1(0)\subset \mathbb{R}^n$ Combining a version of the Hardy inequality, due to Brezis–Marcus, with the mountain pass theorem due to Ambrosetti–Rabinowitz are used to obtain the nontrivial solution. One of the difficulties is to find a range where the Palais Smale converges, because our equation involves a nonlocal term coming from the Kirchhoff term.
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- Copyright © Glasgow Mathematical Journal Trust 2019
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