A CLASS OF CRITICAL KIRCHHOFF PROBLEM ON THE HYPERBOLIC SPACE $\mathbb{H}^{{\it n}}$. (21st January 2019)
- Record Type:
- Journal Article
- Title:
- A CLASS OF CRITICAL KIRCHHOFF PROBLEM ON THE HYPERBOLIC SPACE $\mathbb{H}^{{\it n}}$. (21st January 2019)
- Main Title:
- A CLASS OF CRITICAL KIRCHHOFF PROBLEM ON THE HYPERBOLIC SPACE $\mathbb{H}^{{\it n}}$
- Authors:
- CARRIÃO, PAULO CESAR
COSTA, AUGUSTO CÉSAR DOS REIS
MIYAGAKI, OLIMPIO HIROSHI - Abstract:
- Abstract: 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.
- Is Part Of:
- Glasgow mathematical journal. Volume 62:Part 1(2020)
- Journal:
- Glasgow mathematical journal
- Issue:
- Volume 62:Part 1(2020)
- Issue Display:
- Volume 62, Issue 1, Part 1 (2020)
- Year:
- 2020
- Volume:
- 62
- Issue:
- 1
- Part:
- 1
- Issue Sort Value:
- 2020-0062-0001-0001
- Page Start:
- 109
- Page End:
- 122
- Publication Date:
- 2019-01-21
- Subjects:
- Primary 58J05, -- Secondary 35R01, -- 35J60, -- 35B33
Mathematics -- Periodicals
510 - Journal URLs:
- http://journals.cambridge.org/action/displayJournal?jid=GMJ ↗
- DOI:
- 10.1017/S0017089518000563 ↗
- Languages:
- English
- ISSNs:
- 0017-0895
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD Digital store
- Ingest File:
- 12239.xml