A CLASS OF CRITICAL KIRCHHOFF PROBLEM ON THE HYPERBOLIC SPACE

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 versio...

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Bibliographic Details
Published in:Glasgow mathematical journal 2020-01, Vol.62 (1), p.109-122
Main Authors: CARRIÃO, PAULO CESAR, COSTA, AUGUSTO CÉSAR DOS REIS, MIYAGAKI, OLIMPIO HIROSHI
Format: Article
Language:English
Subjects:
Mountains
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Summary: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.
ISSN:0017-0895
1469-509X
DOI:10.1017/S0017089518000563