Abstract
In this article, we consider the following semilinear elliptic equation on the hyperbolic space ΔHnu - λu + |u|p-1u = 0 on Hn n\{Q} where ΔH n is the Laplace-Beltrami operator on the hyperbolic space Hn = {(x 1, · · · xn, xn+1)|x 1 2 + · · · + xn 2 - x n+1 2 = -1}, n > 10, p > 1, λ > 0, and Q = (0, · · · 0, 1). We provide the existence and uniqueness of a singular positive "radial" solution of the above equation for big p (greater than the Joseph-Lundgren exponent, which appears if n > 10) as well as its asymptotic behavior.
| Original language | English |
|---|---|
| Pages (from-to) | 949-960 |
| Number of pages | 12 |
| Journal | Communications on Pure and Applied Analysis |
| Volume | 13 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2014 Mar 1 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
Cite this
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Existence and uniqueness of singular solutions for elliptic equation on the hyperbolic space. / Wu, Yen Lin; Chen, Zhi-You; Chern, Jann Long; Kabeya, Yoshitsugu.
In: Communications on Pure and Applied Analysis, Vol. 13, No. 2, 01.03.2014, p. 949-960.Research output: Contribution to journal › Article
TY - JOUR
T1 - Existence and uniqueness of singular solutions for elliptic equation on the hyperbolic space
AU - Wu, Yen Lin
AU - Chen, Zhi-You
AU - Chern, Jann Long
AU - Kabeya, Yoshitsugu
PY - 2014/3/1
Y1 - 2014/3/1
N2 - In this article, we consider the following semilinear elliptic equation on the hyperbolic space ΔHnu - λu + |u|p-1u = 0 on Hn n\{Q} where ΔH n is the Laplace-Beltrami operator on the hyperbolic space Hn = {(x 1, · · · xn, xn+1)|x 1 2 + · · · + xn 2 - x n+1 2 = -1}, n > 10, p > 1, λ > 0, and Q = (0, · · · 0, 1). We provide the existence and uniqueness of a singular positive "radial" solution of the above equation for big p (greater than the Joseph-Lundgren exponent, which appears if n > 10) as well as its asymptotic behavior.
AB - In this article, we consider the following semilinear elliptic equation on the hyperbolic space ΔHnu - λu + |u|p-1u = 0 on Hn n\{Q} where ΔH n is the Laplace-Beltrami operator on the hyperbolic space Hn = {(x 1, · · · xn, xn+1)|x 1 2 + · · · + xn 2 - x n+1 2 = -1}, n > 10, p > 1, λ > 0, and Q = (0, · · · 0, 1). We provide the existence and uniqueness of a singular positive "radial" solution of the above equation for big p (greater than the Joseph-Lundgren exponent, which appears if n > 10) as well as its asymptotic behavior.
UR - http://www.scopus.com/inward/record.url?scp=84888177844&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84888177844&partnerID=8YFLogxK
U2 - 10.3934/cpaa.2014.13.949
DO - 10.3934/cpaa.2014.13.949
M3 - Article
AN - SCOPUS:84888177844
VL - 13
SP - 949
EP - 960
JO - Communications on Pure and Applied Analysis
JF - Communications on Pure and Applied Analysis
SN - 1534-0392
IS - 2
ER -