Electron. J. Diff. Equ., Vol. 2010(2010), No. 116, pp. 1-14.

Asymptotic behavior of ground state solution for Henon type systems

Ying Wang, Jianfu Yang

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

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Ying Wang
Department of Mathematics, Jiangxi Normal University
Nanchang, Jiangxi 330022, China
email: yingwang00@126.com
Jianfu Yang
Department of Mathematics, Jiangxi Normal University
Nanchang, Jiangxi 330022, China
email: jfyang_2000@yahoo.com

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