Geodesic
A CLASS OF CRITICAL KIRCHHOFF PROBLEM ON THE HYPERBOLIC SPACE $\mathbb{H}^{{\it n}}$
Glasgow mathematical journal, Tome 62 (2020) no. 1, pp. 109-122

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
CARRIÃO, PAULO CESAR; COSTA, AUGUSTO CÉSAR DOS REIS; MIYAGAKI, OLIMPIO HIROSHI. A CLASS OF CRITICAL KIRCHHOFF PROBLEM ON THE HYPERBOLIC SPACE $\mathbb{H}^{{\it n}}$. Glasgow mathematical journal, Tome 62 (2020) no. 1, pp. 109-122. doi: 10.1017/S0017089518000563
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