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
N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2014/3
Y1 - 2014/3
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 ΔHn is the Laplace-Beltrami operator on the hyperbolic space Hn = {(x 1, · · · xn, xn+1)|x 12 + · · · + 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 ΔHn is the Laplace-Beltrami operator on the hyperbolic space Hn = {(x 1, · · · xn, xn+1)|x 12 + · · · + 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.
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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 -