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