Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 208, pp. 1-13.
Title: Existence and asymptotic behavior of solutions for Henon equations
in hyperbolic spaces
Authors: Haiyang He (Hunan Normal Univ., Changsha, China)
Wei Wang (Hunan Normal Univ., Changsha, China)
Abstract:
In this article, we consider the existence and asymptotic behavior
of solutions for the Henon equation
$$\displaylines{
-\Delta_{\mathbb{B}^N}u=(d(x))^{\alpha}|u|^{p-2}u, \quad x\in \Omega\cr
u=0 \quad x\in \partial \Omega,
}$$
where $\Delta_{\mathbb{B}^N}$ denotes the Laplace Beltrami operator
on the disc model of the Hyperbolic space $\mathbb{B}^N$,
$d(x)=d_{\mathbb{B}^N}(0,x)$, $\Omega \subset \mathbb{B}^N$
is geodesic ball with radius $1$, $\alpha>0, N\geq 3$.
We study the existence of hyperbolic symmetric solutions
when $2