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

DOI

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
@article{10_1017_S0017089518000563,
     author = {CARRI\~AO, PAULO CESAR and COSTA, AUGUSTO C\'ESAR DOS REIS and MIYAGAKI, OLIMPIO HIROSHI},
     title = {A {CLASS} {OF} {CRITICAL} {KIRCHHOFF} {PROBLEM} {ON} {THE} {HYPERBOLIC} {SPACE} $\mathbb{H}^{{\it n}}$},
     journal = {Glasgow mathematical journal},
     pages = {109--122},
     year = {2020},
     volume = {62},
     number = {1},
     doi = {10.1017/S0017089518000563},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000563/}
}
TY  - JOUR
AU  - CARRIÃO, PAULO CESAR
AU  - COSTA, AUGUSTO CÉSAR DOS REIS
AU  - MIYAGAKI, OLIMPIO HIROSHI
TI  - A CLASS OF CRITICAL KIRCHHOFF PROBLEM ON THE HYPERBOLIC SPACE $\mathbb{H}^{{\it n}}$
JO  - Glasgow mathematical journal
PY  - 2020
SP  - 109
EP  - 122
VL  - 62
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000563/
DO  - 10.1017/S0017089518000563
ID  - 10_1017_S0017089518000563
ER  - 
%0 Journal Article
%A CARRIÃO, PAULO CESAR
%A COSTA, AUGUSTO CÉSAR DOS REIS
%A MIYAGAKI, OLIMPIO HIROSHI
%T A CLASS OF CRITICAL KIRCHHOFF PROBLEM ON THE HYPERBOLIC SPACE $\mathbb{H}^{{\it n}}$
%J Glasgow mathematical journal
%D 2020
%P 109-122
%V 62
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000563/
%R 10.1017/S0017089518000563
%F 10_1017_S0017089518000563

Cité par Sources :