Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 116, pp. 1-14.
Title: Asymptotic behavior of ground state solution for Henon type systems
Authors: Ying Wang (Jiangxi Normal Univ., Nanchang, China)
Jianfu Yang (Jiangxi Normal Univ., Nanchang, China)
Abstract:
In this article, we investigate the asymptotic behavior of
positive ground state solutions, as
$\alpha\to\infty$, for the following Henon type system
$$
-\Delta u=\frac{2p}{p+q}|x|^\alpha u^{p-1}v^q,\quad
-\Delta v=\frac{2q}{p+q}|x|^\alpha u^pv^{q-1},\quad \hbox{in } B_1(0)
$$
with zero boundary condition, where $B_1(0)\subset\mathbb{R}^N$
($N\geq3$) is the unit ball centered at the origin,
$p,q>1$, $p+q<2^*=2N/(N-2)$.
We show that both components of the ground solution pair $(u, v)$
concentrate on the same point on the boundary $\partial B_1(0)$ as
$\alpha\to\infty$.
Submitted July 14, 2010. Published August 20, 2010.
Math Subject Classifications: 35J50, 35J57, 35J47.
Key Words: Asymptotic behavior; Henon systems; ground state solution